An overview on the history of actuarial calculus in Portugal until the late 19th century

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An overview on the history of actuarial calculus in Portugal until the late 19th century Ana Patrícia Martins a,b a Centro Interuniversitário de História das Ciências e da Tecnologia - Pólo Universidade de Lisboa, Faculdade de Ciências,

Edif. C4, Piso 3, Gabinete 15, Campo Grande, 1749-016 Lisboa, Portugal b Escola Superior de Educação de Viseu, Rua Maximiano Aragão, 3504 - 501 Viseu, Portugal

Abstract Pension funds, namely survivors’ pension funds were established in Portugal in the late 18th century, in mutual benefit societies. The first Portuguese life assurance companies were created in the first half of the 19th century but their activity was not very extensive. Only in the 20th century did both institutions become actuarially-based. In this paper, we provide an overview of the development of actuarial calculus in Portugal until the late 19th century, in order to contextualise the scientific progress of those institutions, mainly the former. This paper lays the groundwork for further research on the history of actuarial calculus in Portugal. © 2020 Elsevier Inc. All rights reserved. Sumário Os fundos de pensões, designadamente fundos pensões de sobrevivência, surgiram em Portugal em finais do século XVIII. As primeiras companhias de seguros vida foram criadas na primeira metade do século XIX mas a sua actividade não foi relevante. Apenas no século XX os princípios da ciência actuarial passaram a ser usados em ambas as instituições. Neste artigo daremos um panorama do desenvolvimento do cálculo actuarial em Portugal até finais do século XIX, de modo a contextualizar o progresso científico dessas instituições, principalmente das primeiras. Este artigo estabelece as bases para investigações futuras na história do cálculo actuarial em Portugal. © 2020 Elsevier Inc. All rights reserved.

MSC: 01A55; 01A85 Keywords: History of actuarial calculus; Portugal; 19th century; Survivors’ pensions; Life assurance

E-mail address: [email protected]. https://doi.org/10.1016/j.hm.2020.01.001 0315-0860/© 2020 Elsevier Inc. All rights reserved.

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0. Introduction1 The progress of actuarial calculus has not been a favoured topic of researchers on the history of mathematics in Portugal. Classical texts on the historiography of mathematics contain very brief commentaries, with no mathematical substance, on a few contributions to actuarial calculus — those of the mathematician Daniel Augusto da Silva (1814–1878) and of three actuaries, António dos Santos Lucas (1866–1939), Luciano Pereira da Silva (1864–1926) and Fernando Teixeira Homem de Brederode (1867–1939) (the first two, also mathematicians).2 The latest research on the history of mathematics in Portugal also refers to particular contributions on actuarial calculus — (Martins, 2012) is a detailed study on Daniel da Silva and (Martins, 2018a) and (Martins, 2018b) are initial approaches to the works of Pereira da Silva and of the naval officer and mathematician José Maria Dantas Pereira (1772–1836), without analysis of actuarial mathematics’ topics. This paper presents an overview of the history of actuarial calculus in Portugal until the late 19th century with the purpose of contextualising the scientific progress of survivors’ pension assistance and life assurance. Since this is only one contribution in this broad research area, it is inevitable that several subjects are not analysed in depth, or even mentioned in this paper. The Portuguese 19th century began turbulently. Portugal was in a period of political turmoil and economic stagnation, starting with the French invasions (1807–1811), with devastating consequences for the country’s economy and society, the forced exile of the Royal Family to Rio de Janeiro (1807), the subsequent independence of Brazil (1822), the Liberal Revolution that changed the political regime from an absolute to a constitutional monarchy (also in 1822) and the Liberal Wars, opposing liberal constitutionalists and conservative absolutists over royal succession (1828–1834). Soon after the civil war and the restoration of the constitutional regime (1834), the first institutional steps were taken to launch public assistance and regulate private assistance.3 Official intervention was driven by the extinction of the religious orders and arts and crafts corporations in 1834, which had a crucial function in public charity, and the emergence of social problems arising from industrialisation. The insufficiency of social protection mainly felt by the middle-class was the reason for the growth of the mutualist movement. Until the mid-19th century there were 27 mutual benefit societies in Portugal (usually known as montepios), mostly in the Reign’s capital, Lisbon, 19 (70%).4 1 All quotations from Portuguese works appear in English translation made by the author. 2 The mentioned texts were authored by Francisco Gomes Teixeira (1851–1933), Rodolfo Ferreira Dias Guimarães (1866–1918),

Joaquim José Dionísio (1924–1911) and José Tiago da Fonseca Oliveira (1928–1992). On the historiography of mathematics in Portugal see (Saraiva, 2004). On Daniel da Silva, see (Teixeira, 1902), (Dionísio, 1978), (Oliveira, 1989) and (Guimarães, 1909). The last, Les mathématiques en Portugal, is a catalogue of Portuguese texts on mathematics, compiled according to the norms of the 1889 Congrès International de Bibliographie des Sciences Mathématiques and elaborated to be presented at the Paris Universal Exhibition of 1900 (the 1st edition is from 1900, with a slightly different title — Les mathématiques en Portugal au 19ème siècle; this 2nd edition was substantially expanded). On this catalogue see (Saraiva, 1997). On Santos Lucas, Pereira da Silva and Brederode see (Guimarães, 1909). On the developments of mathematics in Portugal in the 19th century see (Saraiva, 2008, 303–305). 3 (Maia, 1985). The foundation of the Conselho Geral de Beneficência (General Charity Council) in 1835 is considered to be the beginning of public assistance in Portugal. The author considers the foundation of Casa Pia de Lisboa in 1780 as the origin of public social assistance in Portugal. 4 (Goodolphim, 1889, 113–114). We find indistinctly the designations sociedade de socorro mútuo (mutual benefit society), associação de socorro mútuo (mutual benefit association) and caixa de socorro (support fund) in the laws promulgated on the occasion of the several inquiries made to those societies, from the 1860s onwards. Montepios provided assistance to members in the case of illness, temporary or even permanent inability to work and old age; the assistance to their heirs was made in the form of a pension. They also promised to secure a decent funeral for their members.

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The principle of association developed in Portugal in the second half of the 19th century, similarly to what happened in Europe, as a consequence of the French Revolution of 1848.5 The number of montepios soared — from 27 to 365 (1252% growth), half of them in Lisbon, 175 (821% growth).6 In the Regeneration period (1851–1868), Portugal experienced a series of administrative and economic-social reforms and conditions were created to ensure the development of industrialisation and infrastructures of transport and communication.7 Despite several crises in Portugal during the three last decades of the 19th century, montepios experienced some progress of a structural nature. Concerning the life assurance industry, the activity of Portuguese companies was not regular during the 19th century. The first initiative occurred in Lisbon, in 1835, at a time when free association flourished, but in the late 1850s life assurance assistance was extinguished and only in the 20th century did a full resumption occur.8 In this paper, we contextualise the scientific progress of Portuguese life assurance companies and mutual benefit societies that provided pensões de sobrevivência (survivors’ pensions), called montepios de sobrevivência — institutions of unquestionable relevance for social assistance. More emphasis will be placed on the latter, since the life assurance industry was not very active until the early 20th century. Our focus will be on institutions established in Lisbon. We endeavour to determine whether pension/life assurance plans of those institutions were actuarially-based and the difficulties involved in developing such a basis — the knowledge of foreign institutions from more advanced countries providing that kind of assistance and life annuity/life assurance theories and the existence of expertise to address those problems. We will also look at identifying contributions to ensure the progress of those institutions — who proposed them, the use of scientific methods, the reception and impact of those contributions, and the role of the Portuguese government, as a regulating and supervising authority. For that contextualisation, several topics must be discussed, namely texts on life annuity and life assurance theories written in Portuguese, Portuguese statistical mortality data and mortality tables, official regulation of montepios and life assurance companies, actuarial education in Portuguese institutions and Portuguese professional associations of actuaries. Some topics, such as professional associations and actuarial instruction (focused in Lisbon) are included as appendices since they go beyond the time-frame of this paper, albeit they are essential to complete the narrative of this paper. Other topics are detailed in the appendices, since they are not essential to argumentation — such is the case with the impact of the Congrès Général de Statistique (International Statistical Congress) on practices in Portugal. In section 1 we provide the framework with which the development of actuarial calculus in Portugal can be placed in comparison with European developments. The focus will be placed mainly on British contributions, reflecting on the development of actuarial science in the United Kingdom, but also French contributions will be mentioned. Some parishes settled its montepios with a charity character, but those associations had a wider representation in civil and military institutions. (Goodolphim, 1889) is an important text on welfare, focusing on the most relevant Portuguese associative institutions dedicated to social security. Costa Goodolphim (1842–1912) was a prominent intellectual who promoted the social role of civil society and was well known for his works on welfare and association. 5 (Goodolphim, 1974) is an extensive text about the association movement, particularly in Portugal, with detailed informations about Portuguese societies from 1838 until the 1870s. 6 (Goodolphim, 1889, 113–114). Those statistics only refer to the period 1851–1889. There was a great concentration of montepios in Lisbon and Porto. Saraiva highlights a correlation between the growth of industry and mutual benefit societies — the entrance in those societies was increased by poor housing conditions, poor working conditions and insufficiency to pay for assistance in disease: (Saraiva, 2011, 65). 7 On the Regeneration period see (Sousa and Marques, 2004) and (Almeida, 1995). 8 On the Portuguese insurance industry, from the Reign of D. Dinis until the late 1980s, see chapter 3 “Os seguros em Portugal” (Insurance in Portugal) of (Sousa and Alves, 1995).

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This paper provides the context and background for subsequent research on the history of actuarial calculus in Portugal until the early 20th century. In a future publication we intend to analyse the contributions of the mathematician Daniel da Silva on actuarial calculus, namely his studies on the financial viability of pension plans set up at montepios de sobrevivência.9 1. Notes on the history of actuarial science Although life assurance has led to an in-depth development of actuarial science, the first application of this science was in life annuities, allowing the calculation of survivors’ pensions offered by widows’ and orphans’ funds. The success of survivors’ pension schemes or life assurance schemes depends on actuarial sound plans — the contribution income should exceed the benefit and expense payments. Basic life annuity theory was already established in the first half of the 18th century. De Moivre wrote the first text on life contingencies, Annuities upon Lives (1725), containing algebraical manipulations to calculate life annuities in several cases. On life assurance, The Mathematical Repository (1748, 1753, 1755), authored by James Dodson, gives the formula for annual premiums differentiated by ages. One of the most popular treatises on life annuity theory, with many applications to actuarial science, was written by Richard Price, Observations on Reversionary Payments; on Schemes for Providing Annuities for Widows, and for Persons in Old Age; on the Method of Calculating the Values of Assurances on Lives (1771). Numerous British authors wrote about life annuity and life assurance theories and in the early 19th century there were numerous texts making it understandable to those who had some mathematical knowledge. In France, with the exception of the emigrated De Moivre, the first contributions in actuarial science were due to Déparcieux and Duvillard, with the construction of mortality tables. Until the 1830s, there were only three French treatises on life annuity. Déparcieux wrote the first, Essai sur les probabilités de la durée de la vie humaine (1746), Saint-Cyran wrote Calcul des rentes viagères sur une et sur plusieurs têtes (1779) and Duvillard wrote Recherches sur les rentes, les emprunts et les remboursements (1787) — the last two with no scientific novelty. Procedures proposed in the second half of the 17th century to calculate the purchase price of a life annuity and insurance products, in the 18th century, were similar — the actuarial models used were determinist, since they did not allow for the riskiness inherent in insurance contracts; age-discrete, since they were not based on mortality laws; single-decrement; assuming homogeneity, although restriction was imposed on health conditions; and static, since dynamic mortality was only achieved with the construction of long series of mortality observations. Although the mathematical foundation of the life annuity theory and life assurance theory is not complex, its use to construct monetary tables involves many calculations. Commutation functions were used to aid in calculations, since computation was still done by hand. Since the first half of the 18th century, treatises on life annuity and life assurance included monetary tables that helped actuarial practices. The Insurance Cyclopædia contains a list of British texts from 1725 until 1870 with monetary tables — 38 references from 33 authors, most of them from the 1820s onwards10 ; we did not find a similar list of French texts. 9 Da Silva was one of the most important Portuguese mathematicians of the 19th century. He was a naval officer, professor at the Escola Naval (Naval School) and member of the Academia Real das Ciências de Lisboa (Royal Academy of Sciences of Lisbon). He had a Bachelors in Mathematics from the University of Coimbra and his scientific texts stand out in mechanics (astatic), theory of numbers (binomial congruences) and actuarial calculus. On da Silva, see (Martins, 2014) (a biography, on the occasion of the bicentenary of his birthday) and (Martins, 2012) (for an overview of his scientific production and details on his instruction, teaching activity, affiliation to scientific and literary institutions and contributions on actuarial calculus). 10 Actuarial tables, in: (Walford, 1871–1880, 1 (1871), 22–26).

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The first European societies providing survivors’ pensions were the widows’ funds — Germany was a pioneer in this regard, in the early 17th century, but we do not know any reference that clarifies the scientific foundation of those German associations. The first French mutual benefit societies date from the late 16th century but it was in the mid-19th century that the industry established its legal regime and first regulation. In that period, a study was made of the French mutual benefit societies, (Hubbard, 1852), and the industry’s lack of scientific foundations was admitted — the organisation of British institutions was used as a model and the advised foundations were based on British treatises. With few exceptions, it was “empirisme” that was present in the establishment of those societies; concerning the foundational principles used, no logical relation was found — “tout est laissé au hasard” — and the consequence was the dissolution of the most part — “beaucoup ont payé leur imprévoyance par des dissolutions prématurées”.11 A few life offices were created in France in the late 18th century but the prohibition of life assurance that lasted until the late 1810s, annulled those initiatives. Duvillard was the responsible for some of those attempts, a fact that highlights the status claimed for him by Guy Thuillier in the book Le premier actuaire de France: Duvillard (1755–1832) (1997). In the 1860s, the legality of life assurance was still in discussion, by virtue of the Ordonnance de la Marine of 1681, which prohibited life assurance — the prevailing opinion was that life could not be an object of trade. Anyway, in the early 20th century it was already a normal feature of society. The first regulation of French life assurance companies was published in 1905, stipulating measures for the proper constitution of mathematical reserves and, concerning the activity of foreign companies, preservation of national capital in France. In the United Kingdom, there were two kinds of societies providing survivors’ pensions — widows’ funds, particularly established in Scotland, and friendly societies. The first widows’ funds were created in the late 17th century and “the true principles on which they should be established were not understood, and, consequently, great difficulty was experienced in adjusting the rates payable by the members to secure the benefits of the fund”.12

The lack of scientific preparation of its founders was recognised — “shrewd far-seeing men, animated by a noble benevolence”, who based the foundations of those societies “on as sound financial lines as were then possible, endeavouring, as best they might, to equate what are the two leading items in all such schemes, viz: Benefit and Contribution”.13

The first actuarially-based widows’ fund was the Scottish Ministers’ Widows’ Fund, founded in 1774, to assist the widows and children of the Ministers of the Church of Scotland and of the Heads, Principals and Masters of the Universities of Saint Andrews, Glasgow and Edinburgh. It was an example of success, since it was extinguished only in 1993 and inspired similar initiatives in the United Kingdom. It was based on the maximum principle, according to which the number of members remained stationary and, consequently, the 11 (Hubbard, 1852, 51, 59, 62). This text is the fruit of a study performed by the Comité pour la propagation des sociétés de

prévoyance, created in 1849, with the purpose of studying the progress of those societies, advising what should be its foundational principles. The text Principles élémentaires de Calcul, included in (Hubbard, 1852) and written by the mathematician, social reformer and banker Olinde Rodrigues is based on British treatises and was recommended to be used by those societies. On Olinde Rodrigues, see (Altmann and Ortiz, 2005). It is possible that, by saying “empirisme”, the author meant that it was just guess work based on some working knowledge. 12 (Huie, 1868, 1). In the late 19th century, this book was considered as a reference for actuaries. Actuarial valuations of widows’ funds are discussed and several marriage statistics tables and corresponding monetary tables are included. 13 (Hewat, 1896, 7). This book is the fruit of an investigation made by the Scottish actuary Archibald Hewat on the Scottish Widows’ Funds and was motivated by the lack of appropriate actuarial tables.

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number of widows would reach a point at which it would neither increase nor decrease.14 The success of that fund is due to the achievement of that goal — there was a guaranteed annual income from contributors and the benefits would gradually increase to a stationary level — and the use of appropriate rates of interest and mortality tables. In the late 19th century, the progress of the widows’ funds was the fruit of fortunate circumstances: the effort of managers, the accumulation of reliable statistics and the efficiency of competent actuaries.15 Friendly societies providing widows’ and children’s pensions were founded in the mid-18th century.16 The first law regulating those societies, the Rose’s Act, came into effect in 1793, and until the 1820s the responsibility for their regulation was debated — the figure of the actuary was initially considered but it was neglected in 1829. The admission of members regardless of age or health condition, and the use of inaccurate contribution or benefit tables by the first friendly societies, led to their insolvency. In the mid-19th century, the unsound status of those societies, the importance of vital statistics for actuarial practices and the urgency of statistical data were recognised: “At present, nothing but arbitrary tests exist, and consequently, all the absurdities of caprice, instability, and prejudice, interpose in the place which should be occupied by the science, judgment, and disciplined skill of the actuary.”.17

In the late 19th century, the presence of professional actuaries was not very welcome within the friendly society movement because, being outsiders, actuaries could reveal the dangers of the use of inadequate tables based on insufficient data. The intervention of the government, requiring periodic reports of societies’ financial returns, was not successful — societies usually evaded regulation. The first British actuarially-based life assurance company was Equitable, founded in London in 1762. The period 1816–1844 is considered the golden age for the insurance industry in England, even though “companies sprang up like gnats on a summer’s evening and disappeared as suddenly”; registration was introduced in the United Kingdom in 1844 and during the bubble years from 1844 to 1862, 90 percent of the life offices went under.18 Many life offices had no professional advice and even with the foundation of the Institute of Actuaries, in 1848, those societies were not immediately scientifically grounded. Supervision of life assurance companies became effective only after the Life Assurances Companies Act of 1870, since it “imposed unprecedented levels of accountability on life offices, monitored future mergers, and made it harder to start up new companies”.19 Mortality tables are one of the crucial factors to have actuarially-based plans and institutions could choose well-known monetary tables to elaborate their pension/life assurance plans, using the similarity between mortality statistical data of their populations and the mortality tables used to construct the chosen monetary tables. British mortality tables were the first to be constructed in the 1660s — Graunt’s mortality tables, using London’s bills of mortality, had a large influence throughout Europe. In the 18th and 19th centuries, there was no other country with as many tables as the United Kingdom, reflecting the development of actuarial science in that country. Northampton Table and Carlisle Table, constructed by Price and Milne, 14 (Dunlop, 1992, 56–76). David Hare and William Scott refer to its pension fund in the chapter “The Scottish Ministers’ Widows’

Fund at 1774. The Earliest Actuarially-Based Fund in the World”. 15 (Hewat, 1896, 9). 16 Historiography suggests that working and middle-class people joined those societies even though there was a numerical minority of the former: (Cordery, 2003, 176). This text is the first monograph on the topic since Gosden’s The Friendly Societies in England 1815–1875 (1861). Four decades between the two books illustrate the difficulty of studying those societies. 17 (Neison, 1857, xiv). 18 (Sibbett, 2004, 801). Sibbett also clarifies that life assurance companies were used by wealthier sections of the society. 19 (Alborn, 2009, 53).

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respectively, and published in 1793 and 1815, were the two most popular English mortality tables, the latter being most used in the second half of the 19th century in the United Kingdom, as well as in the United States of America. British life offices have collected statistical data to calculate mortality tables since 1837 — the first ones, The Seventeen Offices’ Tables, were published in 1843 and The Twenty Offices’ Tables were published in 1869. Until then, actuaries used three sorts of statistical data to construct mortality tables or perform actuarial valuations: local burial and baptism records, surveys of mortality among government annuitants and claims from Equitable. Regarding friendly societies, the first reliable statistics, including life expectancy were collected between 1836 and 1840 by Neison and published in Contribution to Vital Statistics (1845). As for widows’ funds, the first text containing statistical data that could be used to construct monetary tables was published in 1868, authored by the Scottish actuary Huie — Remarks on the Valuation of Widows’ Funds with Tables to Assist the Actuary in Scotland (1868). In Holland, Struick and Kersseboom produced, in the mid-18th century, the first mortality tables separating genders (1740, 1742) — Kersseboom’s table was widely used in Europe, during the 19th century. In France, Déparcieux’s and Duvillard’s mortality tables (1746, 1808) had wide diffusion until the end of the 19th century, despite its lack of accuracy — the first, that also used records from government annuitants, to calculate life annuity and life assurance premiums, and the other to calculate disease insurance premiums. The first French statistics on mutual societies were published by the Comité pour la propagation des sociétés de prévoyance, in the 1850s. The most important and disseminated French mortality tables of the late 19th century were the RF tables (Rentiers français) and the AF tables (Assurés français), approved in the 1890s and produced by the Comité des compagnies d’assurances a primes fixes sur la vie. The 19th century was marked by a rapid expansion of life insurance industry and the beginning of professional associations of actuaries. The first were established in the United Kingdom — the Institute of Actuaries (1848), in London, and the Faculty of Actuaries (1856), in Edinburgh. After them, other European professional associations were founded — in Germany (1868), Holland (1888), France (in 1872, the Cercle des actuaires Français, extinguished in 1880, and in 1890, the Institut des Actuaires), Belgium (1895), Italy (1897), Denmark (1901), Austria (1904), Norway (1904), Switzerland (1905), Czechoslovakia (1919), Poland (1920), Finland (1922), Bulgaria (1924), Portugal (in 1926, the Associação dos Actuários Portugueses, and in 1945, the Instituto dos Actuários Portugueses) and Spain (in 1927, the Asociación Actuarial Matemática Española, and in 1942, the Instituto de Actuarios Españoles). Actuarial education was first introduced in the United Kingdom and the model that was adopted, giving the responsibility to professional bodies of actuaries, was followed by other countries, such as United States of America, Australia, New Zealand, South Africa and Canada; in Continental Europe it was the responsibility of universities or Technische Hochschulen (technical colleges, TC). At the Institute of Actuaries (1848) and Faculty of Actuaries (1856), instruction was given to applicants and examinations were performed to access the profession. In Continental Europe, departments of actuarial mathematics were integrated either in mathematics or economics departments of teaching institutions — the pioneer was the TC of Zurich (1858), followed by the TC of Wien (1892) and the TC of Prague (1895). After those, universities in Göttingen (1895), Utrecht, Rotterdam and Amsterdam (offering several courses between 1896 and 1939), Iowa (1902), Michigan (1903), Copenhagen (1906), Lausanne (1913), Texas (1913), Sydney (1915), Madrid (1915), Oslo (1916), Edinburgh (1918), Stockholm (1929), Lyon (1930), Montreal (1933), Manitoba (1935), Rome (1935), Basel (1938) and Louvain (1938). 2. Progress of montepios de sobrevivência Our focus is on the Portuguese montepios that provided survivors’ pensions for widows and orphans, the montepios de sobrevivência — we studied the pension plans of the most relevant societies settled in Lisbon

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in the 19th century.20 Three of them still exist — Montepio Filarmónico, Montepio Geral and Associação dos Empregados do Estado. Montepio Militar was the first montepio de sobrevivência established in Portugal, in the late 18th century; Montepio Filarmónico was the first civil one; Montepio Geral was, and still is, the most prosperous one (in 2019 Montepio Geral was Banco Montepio). Most of the studied montepios de sobrevivência exclusively served specific occupational groups.21 Montepio Geral was the only one that allowed the admission of any citizen provided his behaviour did not make him “unworthy of admission”; its denomination, Geral, highlights that generality.22 On the occasion of the first Congresso Nacional de Mutualidade (National Congress on Mutuality), held in 1911, one year after the implementation of the Republic, it was clarified that the number of montepios and its constitution were small — the proletariat had no economic power to be admitted.23 2.1. Pension funds and their mathematical bases Pension plans of the studied montepios de sobrevivência had two kinds of rules — either the payments made by each member and the benefit received by the heirs/beneficiaries were calculated in terms of the salary of the member or they depended on the subscribed capital and the number of contributive years. Neither cases considered the age of the beneficiary. In the first group, we find Montepio Militar, Montepio Militar de Marinha, Associação do Montepio das Secretarias do Estado, Montepio Literário, Montepio dos oficiais, criados, criadas e mais empregados da Casa Real and Montepio Oficial dos Servidores do Estado. In the second group, we find Montepio Filarmónico, Montepio das Alfândegas do Reino, Montepio dos Empregados Públicos, Montepio Geral, Associação de Socorro e Montepio Geral de Marinha, Montepio Marítimo e Comercial, Associação de Empregados do Estado and Montepio Comercial.24 In most funds, the choice of several beneficiaries was allowed, which could even change over the years — widow and/or 20 To the list presented in (Goodolphim, 1889, 164) we added some relevant societies that had already disappeared in 1889 —

Montepio Militar, Montepio Militar de Marinha, Montepio Literário, Associação do Montepio das Secretarias do Estado, Montepio do Exército e da Armada and Montepio Marítimo e Comercial. We could not clarify the date of foundation of Associação do Montepio das Secretarias do Estado (the year 1835 is mentioned in (Rosendo, 1996, 302)) and of its first statutes. We also could not clarify the date of extinction of Montepio Militar and Montepio Militar de Marinha (the law of foundation of Montepio do Exército e da Armada suggests that this institution was its successor). We also could not find the date of extinction of Montepio dos oficiais, criados, criadas e mais empregados da Casa Real. (Rosendo, 1996) is an extensive exposition about mutualism in Portugal since the 18th century, with a huge list of mutual benefit societies. 21 Militaries (Montepio Militar, Montepio Militar de Marinha, Associação de Socorro e Montepio Geral de Marinha, Montepio do Exército e da Armada), state employees (Associação do Montepio das Secretarias do Estado, Montepio das Alfândegas do Reino, Montepio Literário / Montepio dos Empregados Públicos, Montepio Marítimo e Comercial, Associação dos Empregados do Estado, Montepio Comercial, Montepio Oficial dos Servidores do Estado), music teachers (Montepio Filarmónico) or employees of the Royal House (Montepio dos oficiais, criados, criadas e mais empregados da Casa Real). 22 In the first decades of its existence there were relevant personalities in different areas of society among its members — professors at institutions of higher education, members of the Royal Academy of Sciences of Lisbon, politicians and members of the government. In the late 19th century and beginning of the 20th century its members were middle-class: militaries (20%), commercial employees (14%), civil servants (14%), merchants (11%), bank employees (6%) and physicians, nurses and dentists (5%): (Pistola, 2017, 217). The collected data refers to members’ professions during the period 1883–1930. Pistola’s dissertation provides a case study of Montepio Geral, from its foundation in 1840 until 1930, focusing on how its governance system and decision-making process contributed to transform that association in the largest montepio in the country. 23 (Dias da Silva, 1911, 98). The author refers to mutualism in life assurance and stresses the importance of developing popular life insurance in Portugal. Republic led to the institutionalisation of relations between the State and mutualism and this Congress was a major debate on social issues and on the role of mutual societies for their resolution. 24 In the case of Associação do Montepio das Secretarias do Estado, the first statutes analysed are from 1845 (Alvará, 23rd December 1845). In the case of Montepio Filarmónico, Montepio das Alfândegas do Reino and Associação dos Empregados do

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Table 2.1 Montepios de sobrevivência established in Lisbon (1790–1867). Association

Foundation

Dissolution

First statutes

Montepio Militar (Military Montepio)

1790

1843?

Law, 26th August 1790

Montepio Militar de Marinha (Military Navy Montepio)

1795

1843?

Law, 23rd September 1795 (Alvará)

Montepio Filarmónico (Philarmonic Montepio)

1834

still extant

Law, 21st April 1834

Associação do Montepio das Secretarias do Estado (Association of the Montepio for State Departments)

1835?

1887

?

Montepio das Alfândegas do Reino (Montepio for the Reign Customs)

1840

1934

Law, 13th December 1844 (Alvará)

Montepio Literário/Montepio dos Empregados Públicos/Montepio Geral (Literary Montepio / Montepio for Public Employees / General Montepio)a

1840

still extant

Decree-law, 25th August 1840 Law, 4th January 1844 (Carta de Lei)

Associação de Socorro e Montepio Geral de Marinha (Benefit Society and General Navy Montepio)

1841

1885

Decree-law, 24th December 1841

Montepio dos oficiais, criados, criadas e mais empregados da Casa Real (Montepio for officers, servants and all employees of the Royal House)

1841

?

Decree-law, 25th January 1842

Montepio do Exército e da Armada (Army and Navy Montepio)

1843

1865

Law, 28th June 1843

Montepio Marítimo e Comercial (Marine and Commercial Montepio)

1849

1867

Law, 6th November 1849

Associação dos Empregados do Estado (Association of State Employees)

1855

still extant

Decree-law, 28th November 1855

Montepio Comercial (Commercial Montepio)

1867

1886

Decree-law, 4th June 1867

Montepio Oficial dos Servidores do Estado (Official Montepio for State Servers)

1867

1934

Decree-law, 22nd November 1870

a In March 1840 the Montepio Literário was founded, which became known as Montepio dos Empregados Públicos, somewhere

between March and August 1840. In 1844, it was renamed as Montepio Geral.

sons, father and/or mother, sisters or even other persons designated by members were allowed to be beneficiaries. Pensions would be suspended in case of unmarried daughters that married, widows that remarried and sons who reached the adulthood. With these rules it was impossible to produce actuarially-based contribution or benefit tables. Estado the analysed statutes are posterior to the first ones mentioned in Table 2.1 (decrees-law, 8th August 1857, 27th June 1857 and 26th January 1861, respectively).

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We will refer particularly to the pension plan of Montepio Geral, the most prosperous of the montepios de sobrevivência in the 19th century.25 This institution was considered an example and its pension plan was used as a model by other associations. Table 2.2 is the contribution table approved in 1844, which lasted until 1902 — contributions depended on the subscribed capital and the age of the member on the moment of subscription. From 1902 until 1922, a similar table was approved. The benefit table, also approved in 1844, and which lasted until 1852, gradated pensions in 11 degrees — pensions only depended on the subscribed capital and the number of contributive years (the 1st degree gave right to a quarter of the subscribed capital and the 11th gave right to half the subscribed capital). Similar benefit tables were used until 1922, the only difference being the number of degrees.26 Only in 1922 contributions and benefits were calculated according to the ages of the member and the beneficiaries.27 We found no evidence of the calculations used to produce any of the tables used at Montepio Geral during the 19th century nor any model of a foreign institution that could have been an inspiration. The same for other montepios de sobrevivência.28 In the 1860s, the pension plan of the oldest one, Montepio Militar, which was used as a model by others, was studied by a commission nominated by the Government and it was concluded that it had no similarity with foreign associations of the kind — namely French, English, Prussian, Italian, Spanish or Brazilian ones.29 Montepio Geral was created in 1840 but deficiencies on its pension plan were denounced since the 1860s and financial problems were predicted. In the 1870s and 1880s some solutions that minimised the effects of those inadequacies and ensured the payment of survivors’ pensions were approved in General Assembly of members, but the acceptance by members was difficult. From the late 1860s until the early 20th century there is evidence that members had difficulties in predicting the future of the institution, when it depended on events evolving life probabilities — they did not accept preventive measures, if a rise of contributions or a reduction of rights was necessary.30 25 On the history of Montepio Geral, see (Lopes de Oliveira, 1940), (Rosendo, 1990) and (Nunes et al., 1994). A recent study on

mutualism and capitalism, focused on that institution is (Pistola, 2017). On its pension plan, more details can be found in (Martins, 2012, 279–292, 324–338, 363–382). The tables approved in the period 1844–1922 are transcribed in (Martins, 2012). 26 From 1852 until 1894 there were 31 pension degrees (until the 11th, the values were equal to the previous ones and from the 12th until the 31st, pensions increased until the total of the subscribed capital); from 1894 until 1922, there were 10 pension degrees (the 10th, gave the rights to half the subscribed capital). 27 A specific table defined the payments that should be made to ensure an annual pension of 100$00 escudos for only one beneficiary, according to his/her age; more beneficiaries were allowed, with a necessary adjustment, and a particular table would be produced by the society. The real (plural: réis) was the unit of currency in Portugal from c. 1430 until 1911. It was replaced by the escudo after the implantation of the Republic (1910). 1 escudo (1$00) = 1000 réis (1$000). 28 We did not study the documental archives of montepios de sobrevivência other than Montepio Geral. 29 At the Montepio Militar, one day of the military’s salary was discounted per month and the beneficiaries would receive, after his death, half the salary. Initially, the beneficiaries were only female — widow, single/widowed daughters, sisters or even the officer’s mother. Montepio Militar had several reforms of its statutes but the essential of pension attribution rules was maintained. In the 1860s, there was the intention of founding another military montepio, the Montepio do Exército, and the commission that studied its project also studied the Montepio Militar: (Anonymous, 1865, 10). This text is the published report produced by that commission, which included António Ladislau da Costa Camarate (1814–1891), major of the Army Staff of Artillery, who had completed the Curso Mathematico (Mathematical Course) at the Academia Real de Marinha (Royal Navy Academy) and studied engineering at the Escola do Exército (Army School) and physics and chemistry at the Escola Politécnica (Polytechnic School); and Domingo Pinheiro Borges (1829–1888), captain of engineers, with a degree in Military Engineering by the Army School, who also studied the pension plan of the montepios de sobrevivência, namely of the Montepio Geral, of which he was a member. Three of Borges’ studies were published — (Borges, 1870), (Borges, 1883) and (da Silva and Borges, 1870) — but their scientific relevance has not been studied yet. We could not determine whether Montepio do Exército was actually founded. 30 (Martins, 2012, 338–341, 371–382). The first documented events are related to the reception of da Silva’s studies on the viability of the pension plan of Montepio Geral at the General Assembly of members, in the late 1860s. In the early 20th century, a committee

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Table 2.2 Contribution table of Montepio Geral, for the subscribed capital of 100$000 réis (1844–1902). Age of the member on the moment of subscription

Admission fee 1st year

2nd year

3rd year

up to 25 “ 26 “ 27 “ 28 “ 29 “ 30 “ 31 “ 32 “ 33 “ 34 “ 35 “ 36 “ 37 “ 38 “ 39 “ 40 “ 41 “ 42 “ 43 “ 44 “ 45 “ 46 “ 47 “ 48 “ 49 “ 50 “ 51 “ 52 “ 53 “ 54 “ 55 “ 56 “ 57 “ 58 “ 59 “ 60

5$000 5$000 5$000 5$000 5$000 5$000 5$000 5$000 5$000 5$000 5$000 5$000 5$000 5$000 5$000 5$000 5$340 5$670 6$000 6$340 6$670 7$000 7$340 7$670 8$000 8$340 8$840 9$340 9$840 10$340 10$840 11$340 11$840 12$340 12$840 13$340

$ $500 1$000 2$000 2$500 3$000 3$500 4$000 5$000 5$000 5$000 5$000 5$000 5$000 5$000 5$000 5$340 5$670 6$000 6$340 6$670 7$000 7$340 7$670 8$000 8$340 8$840 9$340 9$840 10$340 10$840 11$340 11$840 12$340 12$840 13$340

$ $ $ $ $ $ $ $ $ $ $ 1$000 2$000 3$000 4$000 5$000 5$320 5$660 6$000 6$320 6$660 7$000 7$320 7$760 8$000 8$320 8$820 9$320 9$820 10$320 10$820 11$320 11$820 12$320 12$820 13$320

Total

Mensal contribution

5$000 5$500 6$000 6$500 7$000 7$500 8$000 8$500 9$000 9$500 10$000 11$000 12$000 13$000 14$000 15$000 16$000 17$000 18$000 19$000 20$000 21$000 22$000 23$000 24$000 25$000 26$500 28$000 29$500 31$000 32$500 34$000 35$500 37$000 38$500 40$000

$420 $420 $420 $420 $420 $420 $440 $460 $480 $500 $520 $540 $560 $580 $600 $620 $640 $660 $680 $700 $720 $740 $760 $780 $800 $820 $880 $940 1$000 1$060 1$120 1$180 1$240 1$300 1$360 1$420

Management, financial and supervisory positions in montepios de sobrevivência were held by members of those institutions that were elected in the General Assembly of members. Specialised committees that studied, for instance, the profitability of their pension funds, were usually filled by members of the association. Therefore, it was not always secured that those studies were performed by persons with the appropriate skills. At Montepio Geral, several committees studied the viability of its pension plan and among its members there were mathematicians, graduates in commerce, professors at the industrial and commercial institutes, but their authority was not always recognised. Daniel da Silva was one of them and that studied the possibility of changing the benefits of members in order to increase the income of the pension fund, was considered “terrorist”, by unidentified members of the General Assembly of members. Terrorist, because it predicted the necessity of reducing pensions, when evidence showed that Montepio Geral was a prosperous institution.

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two studies that derived from this work were published, (da Silva, 1868) and (da Silva, 1870) (section 2.3). Other figures were Luís Feliciano Marrecas Ferreira (1851–1928), António dos Santos Lucas, Augusto Patrício dos Prazeres (1859–1922) and Caetano Maria Beirão da Veiga (1884–1962), who were relevant personalities in the study of pension plans of montepios de sobrevivência, which we will refer to in the following sections. The need for the services of an actuary are documented for the first time in 1911 and an actuarial department was founded in 1917, originally consisting just of Beirão da Veiga.31 The financial stability of Montepio Geral depended heavily on initiatives other than its pension fund. One of its most important sources of profit was Caixa Económica, created in 1844 with the main purpose of managing small savings and extending its assistance to all layers of the society. The profits of that institution were used for damage control for the deficient organisation of the pension fund of Montepio Geral — for 19 years (1898–1917) it was possible to pay survivors’ pensions.32 That kind of subsidiary source of income was not exclusive to Montepio Geral; in the mid-20th century, the longevity of montepios de sobrevivência is stated in similar terms: “The miracle is explained because the financial stability rests not so much in the greatness of the shares, but in the revenues received from profitable operations performed concurrently with the mutual goals.”.33

During the 19th century the studied montepios de sobrevivência had several reforms of their statutes but there were only small changes to their pension plans and the same method for pension attribution was kept. In the mid-20th century, the lack of scientific basis on the foundation of pension funds, namely survivors’ pension funds continued to be recognised — Beirão da Veiga emphasises, in 1946, the impossibility of assisting with science some of them: “In the statutes of some welfare and mutual institutions, we find provisions that result in complex actuarial problems, because they are the result of clauses containing genuine indeterminacies.”.34

2.2. The role of the Portuguese government The meetings of the International Statistical Congress (ISC) held during the second half of the 19th century were particularly important to mutual benefit societies (appendix A). The organisation of those institutions was discussed for the first time in the second meeting of the ISC, held in Paris, in 1855. In 1863, at the Berlin meeting, an international inquiry was recommended, specifying the information that should be known about different provident institutions — saving banks, mutual benefit societies, retirement funds for old age and life assurance companies.35 The presence of Portuguese delegates in those meetings was decisive for the measures adopted by the Portuguese government concerning montepios. António José d’Ávila (1807–1881) was present in both meetings and in one of his reports, he anticipated the importance of such an inquiry: 31 (Martins, 2012, 382, 292). 32 (Lopes de Oliveira, 1940, 182). 33 (Beirão da Veiga, 1946, 88). 34 (Beirão da Veiga, 1946, 87). Those indeterminacies were the same as the ones pointed out previously in this section — the

possibility of beneficiaries to be defined after the death of the member of the institution or the incorrect calculation of contributions, depending on the age of the member or the subscribed capital. 35 (Engel, 1863, 67–75). The original designations are caisse d’épargne, sociétés de sécours mutuels, caisse de retraite pour la vieilesse and sociétés d’assurances. The latter one includes four types of associations: sociétés d’ assurances à primes fixes autres que celles sur la vie; sociétés d’assurances mutuelles autres que celles sur la vie; sociétés d’assurance sur la vie, à primes fixes; and societés tontinières.

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“It should produce excellent results in our country, since it will show the rapid progress that the association movement has made among us, not only in the capital but also in the province. There are already many montepios and they are spread all over the kingdom, and some of them offer assistance and considerable aid to a great number of families”.36

The inquiries performed by the Portuguese government during the 19th century to montepios are an example of the use of statistics to study the state of the Nation, following the spirit of the ISC.37 The first official inquiry was performed in 1860 — the Government recognised the importance of those associations for welfare and since working classes were beginning to recognise its benefits, their progress should be ensured.38 Information about members and the financial situation of associations were asked, following the recommendation made in the Paris meeting (1855). Despite the simplicity of the questions of the delivered form, a great number of montepios did not return the required elements and the first attempt to collect statistical data failed. The inquiry ordered in November of 1866 (decree-law, 22nd November 1866) was the most important one performed in the 19th century, particularly to montepios de sobrevivência. Once again, the Government admitted the value of montepios, assuming its relevance to mitigate the recognised difficulties of official social protection. Nevertheless, the deadline for its conclusion was inadequate and that shows a complete ignorance of the amount of work actually involved.39 This inquiry had two main goals: to examine the development of montepios and to define measures that the State should undertake to ensure their prosperity. Two commissions were appointed to conduct the inquiry, one in Porto and another in Lisbon, involving important personalities. The Lisbon commission included politicians, members of montepios (mostly of the Montepio Geral), academicians of the Academia Real das Ciências de Lisboa (Royal Academy of Sciences of Lisbon, RASL) and mathematicians (professors at institutions of higher education); the Porto commission had a similar composition but no academicians. In those appointments, one of the recommendations of the ISC made in the Berlin meeting was fulfilled — to enrol the services of specialists from each insurance branch and mathematicians in order to collect, combine and analyse statistical data. The mathematicians of the Lisbon commission were Daniel da Silva and Luís Porfírio da Mota Pegado (1831–1903), members of Montepio Geral.40 We only studied the Lisbon commission, which examined seven districts in the south of Portugal — Lisbon, Leiria,

36 (Ávila, 1864, 76). This is an extent report (110 pages) with transcriptions of interventions made at the ISC, reproduction of

documents and reflections on the effects that could be accomplished in Portugal. 37 For more details, see (Martins, 2012, 256–275). 38 A circular was sent to the Governador Civil (Civil Governor) of each district, imposing that each association should fill in a simple form and send the annual report and annual accounts to the Direcção Geral de Comércio e Indústria (Department of Commerce and Industry). 39 The final report of the investigation had to be sent before the next meeting of the Legislative Chambers, which occurred just over a month later. The next meeting of the ISC was set for September 1867 and that possibly explains the rush to get all of the results. 40 da Silva was a member of the Board in 1864 and was studying the financial viability of the pension plan of Montepio Geral (section 2.3); Mota Pegado had also been a member of the Board and was one of the mathematicians that analysed some of da Silva’s texts. Mota Pegado completed the first year of the Polytechnic School for military officers and engineers. From 1854 until 1856, he taught mathematics in the Real Colégio Militar (Royal Military College) and in 1856 he became a professor of the Polytechnic School. In 1862, he was also nominated temporary teacher of the Liceu Nacional de Lisboa (National High School of Lisbon), where he served until 1886. In 1877, he became a member of the RASL and in 1888 director of the Instituto Industrial e Comercial de Lisboa (Industrial and Commercial Institute of Lisbon).

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Santarém, Portalegre, Évora, Beja and Faro — and was divided into three groups, giving special attention to montepios de sobrevivência.41 We want to highlight two of the twenty questions concerning the scientific foundations of montepios de sobrevivência that should be answered — to determine the bases used to calculate the association fees, according to the announced benefits; and how to advise Public Administration or whether those associations should use specific mortality and sickness tables or not, defining suitable foreign tables for that purpose. General and specific forms were distributed to montepios and they were the most complete during the 19th century, with great concern for the details of their financial situation.42 The report of the Lisbon commission was finished in 1868.43 It refers to ten attached documents that supported the answers to the questions of the inquiry, but those documents were not printed. We could not find the manuscript version of the report in the main Portuguese archives and therefore we cannot specify the actuarial topics investigated by the commission. Our focus will be on the conclusions drawn in the published report.44 Despite the huge, and sometimes insurmountable difficulties in obtaining data from the majority of the montepios, the commission maintained that the collected data could contribute in the future to their rational organisation, which was recognised to be important. It was remarked that only a few montepios answered, a sign of the “great delay in which we find ourselves”, which should be regarded as a “genuine national interest”.45 Favourable and unfavourable factors to the progress of montepios were mentioned.46 It was also concluded that the pension plans of the studied montepios de sobrevivência were incorrectly established — no details are mentioned, just that association fees calculations often depended on the “probable lifetime” and therefore it was wrongly assumed “a certain proportionality in the association fees”. To prevent other montepios de sobrevivência from making the same mistakes, a few studies that could be advantageously 41 Vasco Rosendo says that only the Lisbon commission managed to produce useful work, but he does not give any evidence for

the claim: (Rosendo, 1996, 467). The Lisbon commission was established in November 1866; in December the inquiries were sent to montepios; data analysis was made between December 1867 and February 1868 and the report was concluded in October 1868. The minutes of its meetings can be consulted in Biblioteca e Arquivo Histórico de Economia, Comissão encarregada de estudar a organização das sociedades de socorros mútuos, nomeada por Decreto de 22 de Novembro de 1866, DGCI-RCI-1S//17, “Actas da commissão nomeada pr decreto de 22 de Novembro de 1866”. One of the three groups only studied montepios de sobrevivência (Daniel da Silva, Mota Pegado and Custódio Manuel Gomes (1810–1881), one of the founding members of Montepio Geral who had assumed several administrative positions) and the other two groups studied the other montepios, either of the district of Lisbon or of the other six districts. 42 The required information was in harmony with the recommendations of the ISC given at the Berlin meeting (1863), but the questions were adapted to Portuguese societies. The forms advised by the ISC should consider the following associations: saving banks, loan and credit societies; raw material purchasing associations; direct consumption items purchasing associations; associations for the acquisition and growth of the intellectual capital of its members; instruction associations for workers. The insurance institutions included life insurance coverage and survivors’ pensions, where tontines were included. The Portuguese form considers societies that: pay assistance in illness, pay funeral expenses, provide benefits in the event of physical incapacity, of unemployment or imprisonment, promote education, provide survivors’ pensions or manage industrial companies: (Ávila, 1864, 62–65, 101–107). This form is transcribed in (Martins, 2012, 496–497). 43 That report, with 25 pages, was published in the official journal Diário do Governo, in March 1869, and in (Anonymous, 1878). 44 In what follows, citations are from that publication. 45 Only 135 associations answered (Lisbon, 87; Leiria, 4; Santarém, 6; Portalegre, 3; Évora, 5; Beja, 3 and Faro, 14). 46 The agricultural activity prevailing in Portugal was considered disadvantageous for the prosperity of the Portuguese associations in comparison to those in countries with a significant manufacturing industry, where associations grew more rapidly. Education was underlined as a crucial factor — lack of awareness of the benefits of mutualism, the habit of turning to charity, a passion for games of lottery and fictitious spending needs. Economic difficulties of the poorer classes were mentioned — the lack of associations where pledged loans of small amounts could be granted to the poorer classes, or even the lack of an official bureau that studied those institutions, promoting its improvement and national wide expansion.

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used by similar institutions were referred to.47 The Government should approve the statutes of montepios de sobrevivência, in order to avoid errors arising from the lack of scientific bases or from the “inexperience of the founders”. It was also recognised that foreign mortality tables could not be used by Portuguese montepios de sobrevivência, since the social conditions and geographic characteristics of the country were different. In the absence of proper Portuguese mortality tables, the adoption of those foreign tables was advised, “which present a greater risk in the charges, in order to establish the necessary equation between those charges and the means with which they have to be satisfied”. Nevertheless, it is assumed that there was no foreign table that could be “rigorously applied to Portugal”. The need to collect national statistical data in order to construct mortality and disease tables concerning the Portuguese population was also emphasised.48 The disregard for the efforts made by the Lisbon commission was shown in the foundation of an official montepio de sobrevivência even before the investigation was concluded. Montepio Oficial dos Servidores do Estado was founded in June 1867, half a year after the commission was nominated and one and a half years before the conclusion of the investigation.49 Another evidence of the Government’s disengagement and commitment for issues concerning mutual benefit societies is that the report made by the Lisbon commission was not presented or offered to the ISC, when Portuguese delegates had been present in the last two meetings (1872, 1876) and many other publications were offered (appendix A). The inquiry in 1866 did not achieve the expected results. Although it was concluded that pension plans of montepios de sobrevivência were not scientifically based, the commission failed one of the main tasks, the choice of mortality and sickness tables in order to produce appropriate contribution and pension tables. Nevertheless, there were no conditions to accomplish that — statistical data about the Portuguese population began to be collected according to the ISC guidelines from 1864 and the first comparative study of the Portuguese population was only published in 1869, (da Silva, 1869) (section 2.3). Evidence suggests that recommendations made by the Lisbon commission were the only possible — data collection procedures should continue, institutions should be made aware of the importance of answering inquiries towards the elaboration of specific mortality tables in the future, and the foreign mortality tables should be carefully chosen. In the 1870s and 1880s, new attempts to collect statistical data about montepios were ordered but again they were unsuccessful. In 1886, a similar inquiry to the one in 1866 was performed and in the law that enacts it, the inefficiency of all the previous attempts was recognised.50 It was also stressed that previous recommendations on the use of specific scientific texts had been ignored to lay sound foundations for montepios de sobrevivência, as well as to ensure the progress of the existing ones. Even though those texts are not specified, in 1886 there were only four published texts in Portuguese about pension plans of montepios de sobrevivência — three were authored by Daniel da Silva and one by Marrecas Ferreira; two 47 Although those studies are not identified in the report, we know which texts were discussed by the commission — (da Silva,

1868) and (da Silva, 1867), both authored by Daniel da Silva, particularly addressed to Montepio Geral and Montepio Geral de Marinha, to which we will refer in section 2.3. Nevertheless, nothing is said about how those texts could be used. Its adaptation to other montepios de sobrevivência was not an easy task — specific statistical data was necessary to adopt actuarial tables, but even so, many calculations were necessary. The simplest solution for similar associations was to adopt its pension and contribution tables. 48 Other less relevant measures, involving future legislation on montepios de sobrevivência, were advised — obligation of checking physical constitution of prospective members, correctness of accounting and rules for amending the statutes. 49 On Montepio Oficial dos Servidores do Estado and its pension plan, see (Martins, 2012, 292–296). We think that the date of the next ISC meeting, September 1867, possibly influenced the urgency of founding that montepio. The pension plan of that association had no scientific basis — contributions paid by members and the pensions received by beneficiaries were calculated in terms of the salary of the member. Around a decade later, financial problems were identified and government grants became necessary. 50 Decree-law, 2nd December 1886.

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of them on the sustainability of Montepio Geral and two general studies (section 2.3). We did not find evidence indicating whether or not the collected data in this inquiry was studied. The need for regulation of montepios de sobrevivência had been recognised since the inquiry of 1866 but despite the great effort involved in the different inquiries performed in the 19th century, the first regulation of Portuguese montepios was only approved in 1891.51 Nevertheless, nothing was said about what scientific bases should be adopted by societies providing survivors’ pensions. It was admitted that the lack of mortality or sickness tables prevented the definition of those scientific principles, a reason that had been mentioned since the inquiry in 1866. Statutes’ approval became a responsibility of the Ministério das Obras Públicas, Comércio e Indústria (Ministry of Public Works, Commerce and Industry), but that task was not attributed to a specialised technician, an actuary; statutes should be accompanied with “a note summarising the calculations” that served to establish the membership charges and benefits. Five years later, a draft act amending the previous regulation confirms the same obstacles to ensure scientific foundations for montepios de sobrevivência — the selection of a suitable foreign mortality table by each association continued to be recommended, but the insufficiency of statistical data for a proper choice was recognised.52 By the end of the 19th century, the Government continued to give to each montepio de sobrevivência “freedom of choice to choose means to reach the crucial financial balance”. Statistical data collected in the several inquiries to montepios de sobrevivência performed during the 19th century were not used to perform any study on the population of those societies. The first contributions on the construction of Portuguese mortality tables occurred in the mid-1940s. The journal Boletim, published by the Instituto dos Actuários Portugueses (Institute of Portuguese Actuaries), documents those attempts — five articles published from 1946 to 1951, written by graduates in mathematics: (Morais, 1946), (Carvalho and Borralho, 1947), (Horta and Leão, 1948), (Santos, 1951) and (Franco and Costa, 1951).53 2.3. The assistance of science During the 19th century, survivors’ pension plans established at the Portuguese montepios de sobrevivência were not scientifically based — the calculation of contribution and benefit values was hampered by an unusual feature of pension attribution, the possibility of having several beneficiaries besides the widow of the member, but also by the heterogeneity of the members, in terms of their professions and ages. These institutions faced financial problems, having difficulties in paying pensions to the heirs of members (section 2.1). Admission to montepios de sobrevivência was not compulsory and thus it was not certain whether or not the number of members would reach a stationary level. Therefore, the maximum principle used by some Scottish widows’ funds could not be ensured (section 1). Nevertheless, it is a fact that until the 1860s there were no credible mortality statistics for the Portuguese population (generic or relative to specific montepios de sobrevivência) that could be used to choose the most appropriate foreign mortality table to produce actuarial tables using life annuity theory or to choose the most suitable monetary table between the foreign tables that were published from the beginning of the 18th century. The first comparative statistical study of the Portuguese population was performed in the late 1860s, but even its usefulness was diminished by the lack of assiduous procedures of data collection by most of the montepios de sobrevivência (we will refer to that study, performed by Daniel da Silva, in this section). In the late 18th century, at a time when the only Portuguese montepios de sobrevivência were military ones, serving the Army and the Navy (Table 2.1), but with unsound pension funds, the first text on life annuities written in Portuguese was published — a translation by the naval officer Dantas Pereira of the 51 Decree-law, 28th February 1891. 52 Decree-law, 2nd October 1896. 53 The first and the last texts are studies about the Portuguese population and the other three are focused on mutual benefit societies.

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French text Calcul des rentes viagères sur une et sur plusieurs têtes (1779), authored by Saint-Cyran.54 It was published in 1797, nearly two decades after the original text, with the title Calculo das pensões vitalicias por Saint-Cyran (Life Annuities Calculations by Saint-Cyran) — (Saint-Cyran, 1797). Saint-Cyran was one of the authors Dantas Pereira read when he was preparing a “comprehensive elementary text” ordered by Prince D. João (1767–1826, King D. João VI from 1816 to his death).55 On the reasons for choosing the topic of life annuities, he criticises some magistrates for hesitating in applying resolutions “whose exact compliance requires several concepts related with probabilities of human life”. Although it has no scientific novelty, Saint-Cyran’s text was one of the few French contributions on actuarial science in the 18th century (section 1).56 An appendix is added to the original text, which shows the intention of promoting the use of this text — it contains six tables of compound interest, discounts and annuities, elaborated by Price, explaining and exemplifying those concepts; Halley’s mortality table and the Northampton mortality table. We find it possible that, with this translation, Dantas Pereira intended to disseminate the life annuity theory throughout Portugal and strengthen its implementation. We found no explicit reference to the use of Pereira’s translation. This was the only contribution of Dantas Pereira on topics of actuarial science.57 The existence, in the late 18th century, of a text in Portuguese exposing life annuity theory for its simplest cases possible was of the utmost importance for the pension plans set up at montepios de sobrevivência. 54 Dantas Pereira completed the Mathematical Course at the Royal Navy Academy, with a distinction in mathematics. He taught

mathematics at the Academia Real dos Guardas Marinhas (Royal Academy of Ensigns) from approximately 1791 until 1807, when the Companhia dos Guardas Marinhas (Ensigns Corps) moved to Rio de Janeiro, Brazil. In 1807, he became the first director of the Royal Academy of Ensigns. He was a member of the Sociedade Real Marítima (Royal Maritime Society) and of the RASL and published two mathematical articles in the Memoirs of that scientific society. His writings include several areas, illustrating a wide multiplicity of interests: mathematics (life annuities, arithmetic, calculus), nautical topics (nautical ephemeris, naval tactics, hydrography), naval legislation, politics and pasigraphy. In 1834, he went into exile to England and after to France (Paris). On Dantas Pereira, see (Guedes, 1974) and (Almeida, 2018). Calcul des rentes viagères, (Saint-Cyran, 1779), has two parts. The author claims that the first part is elementary, in order to serve its readers who were not versed in algebra and “combinações” (combinations), perhaps clerks of mutual benefit societies, life assurance companies or tontines. It gives a comprehensive view on life annuity theory and how to use life annuity tables. The second part details life annuity theory depending on one, two or more people and uses algebraic notation. Reversionary life annuities, in which the order of survival is considered, are not analysed. 55 Curso de estudos para uso do Commercio, e da Fazenda (Course of Studies for Use in Commerce and Finance) (1798). This is a huge book with over 600 pages. The mathematician Francisco Borja Garção Stockler (1759–1829) wrote the first 244 pages. Stockler is an outstanding figure in the Portuguese scientific scene of the late 18th century and early 19th century. He wrote mathematical works on analysis and history of mathematics and also a detailed plan for the reorganisation of public instruction. On Stockler, see (Saraiva, 1993, 417–419). 56 The subject, rentes viagères, was unfamiliar to the French government and to the public, reasons that justified its publication by the Académie Royale des Sciences. Although we do not know when Dantas Pereira began the translation, in 1797, two other texts written by French authors, on the same subject, had already been published – Déparcieux’s Essai sur les probabilités de la durée de la vie humaine (1746) and Duvillards’s Recherches sur les rentes, les emprunts et les remboursements (1787). Nevertheless, Déparcieux’s text does not have a formula to calculate pensions for more than two beneficiaries and Duvillard’s extensive use of algebraic notation could obstruct one’s understanding and application of the theory. There were numerous British authors that could also have been used by Dantas Pereira, namely Price’s Observations on Reversionary Payments (1771). 57 He translated another text on insurance topics, namely marine insurance, when he was already in Brazil. Reflexões sobre o Commercio dos Seguros (Considerations on Insurance Business) — (Anonymous, 1810) — was published anonymously in Rio de Janeiro and has two parts: the first, “Discurso Relativo aos Seguros em Geral, e aos Navaes em Particular” (Discourse on Insurance, in General, and on Marine Insurance, in Particular), was written by Dantas Pereira and the second is a translation of the article “Assurances maritimes”, written by Condorcet. This text was also ordained by the monarch and reveals a particular interest in the progress of the Nation, since marine insurance contributed to the prosperity of commercial activity which was flourishing in Brazil in the early 19th century. It also fills a gap of texts on insurance topics written in Portuguese. On this text, see (Martins, 2018b). A study of the importance of this translation for the progress of the insurance industry in Brazil has not been made yet.

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At least from the 1840s onwards it was recognised that the pension plans of Portuguese montepios de sobrevivência were not scientifically based. Some authors emphasised it and the criticism they gave shows that they were familiar with the principles of actuarial science. The following examples show the authors’ intention of denouncing official initiatives that compromised official social protection. In the 1840s, Cláudio Adriano da Costa (1795–1866) criticised the generality of the montepios de sobrevivência — its founders were “unaware of the principles prescribed by science” — and particularly about the official institution Associação do Montepio das Secretarias do Estado, designed for employees of the State, he says: “It was sufficient to have the faintest notion of the law of mortality in order not to admit the uniformity of contributions, depending on the salary, disregarding the age of the subscriber.”.58

In the 1860s, Daniel da Silva, for whom montepios de sobrevivência should be “a kind of life assurance, in which everything is formulated according to the principles of probability calculus”59 , denounced the foundational principles of Montepio Oficial dos Servidores do Estado and made a comparison with English institutions: “In England, a classic country of philanthropic institutions, both official and unofficial, there is no evidence that there are any examples of this kind, where the order of succession of pensions is described a priori in the statutes, as occurs among us, without a choice from the subscribers. From this powerful homologation, which we intend to make, of the distinct interests of the different families, it is apparent that a part of the subscribers pay much more, and another much less, then the calculation of the probabilities indicates is necessary for each to guarantee to their natural or legacy heirs, the subsidy to ensure them.”.60

Scholars also recognised that, in order to ensure the progress of montepios de sobrevivência, it was necessary to eliminate the former foundational principles of pension plans, namely the possibility of defining several beneficiaries, and have in consideration the ages of the member and the beneficiary when calculating actuarial tables, but no changes were made throughout the entire 19th century. Evidence shows that they presented proposals which minimised the effects of those plans. The originality and novelty of those contributions, particularly those of Daniel da Silva, rests precisely in the use of concepts of life annuity theory and financial calculus to produce methods that were adapted to the complex and unscientific organisation of pension plans of montepios de sobrevivência. The factors that contributed to this adaptation were the impossibility of proposing actuarially-based pension plans (due to the lack of reliable statistics of the population) and the strong resistance of members to change the statutes. 58 (Anonymous, 1846, 11, 13). This text is a compilation of documents related to the foundation of the life assurance company

Providência, proposed by da Costa (section 3.1). In the mid-1840s montepios de sobrevivência were the only Portuguese institutions providing assistance on lives and Da Costa clarifies that some official montepios had been founded without respecting the principles of science, with consequences on its financial stability. 59 (Anonymous, 1867b). 60 (Anonymous, 1867a). da Silva wrote, anonymously, six articles in Jornal do Commercio, denouncing the foundation of the official institution Montepio Oficial dos Servidores do Estado. For more details see (Martins, 2012, 342–348). Similarly as for other montepios de sobrevivência (section 2.1), at Montepio Oficial dos Servidores do Estado it was possible to have several beneficiaries that could even change over the years. They could be the widow of the member or his sons (unmarried daughters; widowed daughters, without subsistence; minor son; son until age 21, if he was a student with school achievement or had any scientific, literary or artistic profession; adult son with mental disability or physical impossibility; or illegitimate children, if there were no lawful children). If there were none of the previous beneficiaries, it was possible to give pensions to the widowed mother of the member or his spinster or widowed sister or his minor brothers.

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Daniel da Silva became interested in the study of the viability of pension plans of montepios de sobrevivência when he joined Montepio Geral, in 1863. His motivation was to solve the financial instability of the institution as he predicted a bankruptcy.61 Although his interest was related to a particular institution, soon after his special studies became a reason for his nomination as a member of the commission that in 1866 studied the progress of montepios de sobrevivência (section 2.2). That nomination was intended to gather experts that could not only study the progress of those institutions but also advise the Government about the most appropriate measures to ensure their prosperity. The choice of Daniel da Silva shows a recognition of his expertise. The generic studies made by Daniel da Silva in that commission and the particular studies of the pension plan of Montepio Geral and Montepio Geral de Marinha led to the publication of four texts, between 1867 and 1870, related to the viability of pension plans of montepios de sobrevivência — two papers in the Jornal de Sciencias Mathematicas, Physicas e Naturaes (Journal of Mathematical, Physical and Natural Sciences) of the RASL62 and two booklets published at the expenses of Montepio Geral. The mathematician wrote the first comparative study of the Portuguese population, published in 1869, “Contribuições para o estudo comparativo do movimento da população em Portugal” (Contributions for the comparative study of the population in Portugal) — (da Silva, 1869). The goal of this study was to provide a (scientific) basis that could guide the choice of the most suitable foreign mortality table to calculate contribution or benefit tables to be used by montepios de sobrevivência. Official statistical data collected from the 1860s became more credible and da Silva used it to comment general statistics and, concerning mortality statistics, he also used accurate data from two montepios de sobrevivência founded in the 1840s, of which he was a member — Montepio Geral and Montepio Geral da Marinha. He compared mortality statistics from those societies with Portuguese official statistics and foreign statistics, the latter discussed by several relevant experts.63 Montepio Geral was the most successful of those Portuguese societies, which is the reason why that study could be used as a reference by similar institutions, namely those whose members had similar characteristics (for example, age, profession and health conditions). In order to make that comparison, it was important that each society could characterise their group of members but inquiries performed during the 19th century show that many of the montepios de sobrevivência did not collect statistical data about their members (section 2.2). There is no evidence of the use of da Silva’s study, except for the actuarial valuation that he performed on the pension plan of Montepio Geral, which we will refer to briefly in the following. Montepio Geral and Montepio Geral de Marinha had only existed for two decades and their population was not stationary, since admission was not compulsory — therefore, the use of their statistical data in order to choose a reliable foreign mortality table should be made with some caution.64 “Amortização annual media das pensões nos principaes montepios de sobrevivencia portuguezes” (Mean annual value of amortisation of pensions used in the main Portuguese Montepios de sobrevivência) — (da Silva, 1867) — is focused on amortisation of pensions, the core concept of da Silva’s method to perform actuarial valuations of pension plans established at montepios de sobrevivência. Two particular institutions were studied in more detail — Montepio Geral and Montepio Geral de Marinha. The other two texts of da Silva are focused on the study of a particular pension plan, that of Montepio Geral, and were motivated by the financial instability of the institution that was identified in the 1860s. Performing an actuarial valuation, he concluded that “the prosperity of MontePio Geral is quite simply an 61 On da Silva’s contributions on actuarial calculus see (Martins, 2012). 62 On the beginnings of this journal, see (Saraiva, 2005, 170–175). 63 The most part of the authors are just listed, their texts are not referenced: Hubbard, Déparcieux, Quetelet, Duvillard, Montfer-

rand, Kersseboom, Sussmilch, Wargentin, Murnet, Halley, Farr, Milne and Finlaison. 64 On that topic, da Silva refers to Déparcieux’s data collection on French tontines, and stresses the reliability of his mortality

table: “the safest way to produce a reliable life table, or mortality table, is to prefer the observation of a certain number of facts, despite being relatively few, but whose accuracy cannot be doubtful” (da Silva, 1869, 291).

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illusion”, and proposed measures to save the association from a predicted bankruptcy.65 O presente e o futuro do Monte Pio Geral (The Present and the Future of Monte Pio Geral) — (da Silva, 1868) — was written between 1863 and 1865 and in 1870 an improvement of that study was published, Das condições economicas indispensaveis á existencia do Monte Pio Geral (On the Economic Conditions Necessary to the Existence of Monte Pio Geral) — (da Silva, 1870) — using the first two texts mentioned above. These texts are based on the principles of life annuity theory exposed in English and French treatises — (Baily, 1810), (Milne, 1815), (Grémilliet, 1823) and (Hubbard, 1852). The relevance of da Silva’s texts was recognised by a few members of the Montepio Geral, very few of them with significant mathematical knowledge. Da Silva proposed a reform of the pension plan, which was accepted, but not without serious criticism from a large number of members, since their privileges were diminished and their contributions were increased. Da Silva’s studies are relevant because in Portugal there had been no studies before of the financial viability of pension plans of montepios de sobrevivência. Although his methods could be adapted to some of those institutions, the need for reliable statistical data about the members of each montepio and the enormous amount of calculations needed could limit its use. Alternatively, da Silva’s texts could be used as a reference by institutions similar to Montepio Geral and Montepio Geral de Marinha, namely by adopting their contribution or benefit tables. The contribution of Marrecas Ferreira, Estudo sobre monte-pios (Studies on Mutual Benefit Societies) — (Marrecas Ferreira, 1886) — also has the intention of minimising the incorrect mathematical bases of pension funds settled at montepios de sobrevivência.66 A study on its scientific relevance has not been made yet. That study was drafted for the application for the position of Full Professor (lente catedrático) of Financial Operations in the Instituto Industrial e Comercial de Lisboa (Industrial and Commercial Institute of Lisbon, ICIL), where actuarial instruction in Portugal began (appendix B). This text, the only known text of Marrecas on topics of actuarial science, indicates deep knowledge about the unsound pension plans of montepios de sobrevivência, and it was made at a time when the most prosperous institutions of the kind, Montepio Geral and Montepio Oficial dos Servidores do Estado, had financial problems. He was a member of the former and in the 1880s took part in several committees that studied its pension plans.67 The relation between practice, research on actuarial foundations of pension plans of montepios de sobrevivência, and actuarial instruction is suggested in the use of the text Estudo sobre monte-pios for the elaboration of the programme of the 28th subject (Financial Operations) of the ICIL, also authored by Ferreira (appendix B). The successors of Marrecas Ferreira in that position, Prazeres and Beirão da Veiga (appendix B), also stood out in the study of the financial viability of pension plans of montepios de sobrevivência, particularly of Montepio Geral.68 These examples, to which we add those of Daniel da Silva and Santos Lucas, illustrate

65 (da Silva, 1868, 7). 66 Marrecas Ferreira was an officer of the Army who studied at Polytechnic School and Army School, where he completed a

degree in Military Engineering, in 1875. He became professor at the Instituto Industrial e Commercial de Lisboa (Industrial and Commercial Institute of Lisbon) in 1888 and retired in 1923 (appendix B). He was one of the authors of an important regulation of the insurance industry set up in 1907 (section 3.2). In 1926 he was a founding member of the Associação dos Actuários Portugueses (Association of Portuguese Actuaries). Ferreira was nominated president of the Associação dos Engenheiros Civis (Civil Engineers Association), president of the Associação Industrial de Lisboa (Lisbon Industrial Association), president of the Associação Industrial do Porto (Porto Industrial Association) and president of the Real Associação de Agricultura (Royal Agriculture Association). 67 (Martins, 2012, 378–382). 68 Prazeres was considered “the most courageous and valiant pioneer of Portuguese actuarial technique”: (Beirão da Veiga, 1945, 257). He was very active: responsible for the organisation of several financial institutions and banks; one of the authors of the regulation of the insurance industry in 1907 (section 3.2); member of the Comité Permanent des Congrès Internationaux d’Actuaires, since 1908. He was trained at the ICIL, in the Curso Superior de Comércio (Higher Course in Commerce). He taught at the ICIL and at the HIC until 1922 (appendix B).

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that the exercise of actuarial profession in montepios de sobrevivência began to be performed by persons with different academic abilities, mainly mathematicians and those with a degree in Commerce.69 Instruction in actuarial topics taught from the 1880s to the 1910s at the different institutes of Lisbon appears to have been very similar and adjusted to the employability of actuaries — in life insurance companies, montepios de sobrevivência or banks (appendix B). In the late 1930s and 1940s, instruction provided at Lisbon on relevant areas of the life insurance industry and the mathematical theory of financial operations was severely criticised and the foundation of the Centro de Estudos de Matemáticas Aplicadas à Economia (Centre of Mathematical Studies applied to Economics, CMSE) in 1938 was seen as “a way to remedy the evil” (of inappropriate instruction).70 Among the three founding members of CMSE, professors at the Instituto Superior de Ciências Económicas e Financeiras (Higher Institute of Economic and Financial Sciences, HIEFS), there were two mathematicians — Bento de Jesus Caraça (1901–1948) and Aureliano de Mira Fernandes (1884–1958) — and a graduate of the Higher Course in Commerce — Beirão da Veiga.71 The contributions to actuarial science of these three eminent men have not been studied yet. Actuarial education in Portugal followed the pattern of most European countries — it was the responsibility of technical schools and was regulated by the government. 3. Progress of Portuguese life assurance companies During the 19th century, survivors’ pensions assistance in Portugal were provided mainly by montepios de sobrevivência but, just like in other European countries, it was common practice in Portugal that life assurance companies also offered that kind of assistance. The first Portuguese life assurance companies were created in Lisbon — Fidelidade and Providência, in 1835 and 1845, respectively — and Claúdio Adriano da Costa, a relevant figure of the 19th century Beirão da Veiga was trained in 1904 at ICIL, also in the Higher Course in Commerce. He taught at the ICIL, HIC and at the Instituto Superior de Ciências Económicas e Financeiras (Higher Institute of Economical and Financial Sciences). He was director of the HIC and a founding member of the Centro de Estudos de Matemáticas Aplicadas à Economia (Center of Mathematical Studies Applied to Economics) in 1938 (appendix B). He was also very active: he produced reports for life assurance companies; in the 1920s, he was a member of commissions for legal and technical reviews of insurance industry legislation; he wrote texts on actuarial topics, both technical and with promotion purposes of the actuarial activity; he gave several lectures; he was a member of the Comité Permanent des Congrès Internationaux d’Actuaires since 1908, a founding member of the Association of Portuguese Actuaries, created in 1926 (vice-president of the Board), and also a founding member of the Institute of Portuguese Actuaries, founded in 1945 (president of the Board) (appendix C). 69 Santos Lucas was a member of Montepio Geral and in the 1910s he set up committees specially nominated to calculate the mathematical reserves and propose a reform of the statutes: (Martins, 2012, 381). It seems that Lucas’ actuarial activity was more significant in life assurance industry — we will refer to him in section 3.3. We would just like to emphasise here that Lucas was a Doctor in Mathematics at the University of Coimbra. 70 (Beirão da Veiga et al., 1938, 208). 71 Caraça was a mathematician, professor, anti-fascist resistance fighter and militant of the Partido Comunista Português (Portuguese Communist Party). He graduated in 1923 from the HIC but he was a lecturer for subjects of mathematics from 1919. He became Full Professor of the HIEFS in 1930 until he was dismissed, for political reasons, in 1946. He was one of the founding members of the Sociedade Portuguesa de Matemática (Portuguese Society of Mathematics) and the journal Gazeta de Matemática, in 1940. Caraça performed actuarial supervision in several mutual benefit societies, including Montepio Geral, and banks. He was a founding member of the Institute of Portuguese Actuaries, in 1945 (appendices B, C). On Caraça, see http:// casacomum.org/cc/arquivos?set=e_2201, the digitalisation of Caraça’s documents owned by the Fundação Mário Soares (Foundation Mário Soares). Mira Fernandes became a Doctor in Mathematics in 1911 at the University of Coimbra and taught at the Instituto Superior Técnico (Higher Technical Institute) until the jubilation in 1954, where he taught courses on analysis and rational mechanics, and at the HIC from 1918 onwards. He was a member of the RASL and the Real Academia de Ciencias Fisicas y Naturales de Madrid (Royal Academy of Physical and Natural Sciences of Madrid). His research was on differential geometry, mechanics and mathematical topics on the theory of relativity. On Mira Fernandes, see (Saraiva and Pinto, 2010).

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Portuguese economic and business world, was connected to both.72 Da Costa was aware of the progress of the life assurance industry in Europe, he was familiar with the relevant texts and authors on life annuity and life assurance theories and aimed to establish life assurance assistance in Lisbon, on a scientific basis. Those companies did not have a considerable activity in the life assurance industry and it is not even certain if anyone actually subscribed to that coverage. Life assurance industry only had a significant development in Portugal in the early 20th century and therefore the study of the progress of Portuguese life assurance companies during the 19th century should be focused on da Costa’s contributions. A study of the relevance of his contributions to actuarial science has not been made yet. 3.1. Life assurance companies and the mathematical bases Fidelidade was created at a time when there were only three insurance companies operating in Lisbon (one providing fire insurance, one maritime and one both).73 The first statutes of Fidelidade established the possibility of offering life assurance coverage, after the approval of a special regulation that should be made.74 The publication Considerações submettidas à Assemblea Geral da companhia de seguros Fidelidade sobre seguros de vida pela direcção de 1835–1836 (Considerations Submitted to the General Assembly of the Insurance Company Fidelidade by the Board of 1835–1836) — (Companhia de Seguros Fidelidade, 1836) —, proves that intention. We find it possible that da Costa was the main author of this text — not only was he a member of the Board and of several committees that studied the progress of life assurance in Fidelidade, but he also made specific studies on the theme in order to create a new life assurance company, Providência, to which we will refer in the following. The Board of Fidelidade was perfectly aware of the difficulties of establishing that assistance on “mathematical foundations” — one of the main causes pointed out was “we do not have any tables in Portugal that give us the average duration of human life, nor even any which divide ages, with at least a ten-year period”.75 The British reality was considered as an example. Those considerations on life assurance are supported by an extensive exposition of the history of life assurance (38 in a total of 43 pages), emphasising the importance of mortality tables, contributions from the United Kingdom, France and Holland and listing British companies currently operating in the United Kingdom.76 Contributions of Portuguese authors are also mentioned — “some very poor works” on Portuguese mortality statistics.77 Calculation of premium 72 Da Costa was José Ignacio da Costa’s son, former Ministry of Finance. His academic instruction is unknown, but he had a

great intellectual capacity, critical thinking and scientific curiosity. He knew Latin and spoke several modern languages. He was connected with important Portuguese institutions — business companies, insurance companies and gas and electricity companies. His texts on the economic and social field are the most relevant in his time and they have been widely studied by António AlvesCaetano. (See Alves-Caetano, António, 2013. António Alves-Caetano. https://sites.google.com/site/antonioalvescaetano/home.) 73 (Alves-Caetano, 2000–2002, I, 12–13). Alves-Caetano is the author of a very complete and reliable analysis documentation of Fidelidade, in two volumes — (AlvesCaetano, 2000–2002). It contains extracts of the first reports performed by the Board. 74 Law, 29th October 1835 (Portaria). 75 (Companhia de Seguros Fidelidade, 1836, 4). 76 The most part of the authors are just listed, their texts are not referenced: Déparcieux, Condorcet, Laplace, Duvillard, SaintCyran, Messance, Saint-Maur, Montucla, Kersseboom, Simpson, Halley, Morgan, Price, Baron Masères, Hutton, Baily, Smart, Short, Milne, Finlaison, Babbage and McCulloch. 77 The first is “Taboa da lei de mortalidade da especie humana deduzida das observações e calculos feitos por M. Duvillard sobre a povoação de França” (Mortality table for the human kind deduced from the observations and calculations produced by Mr. Duvillard about the population of France), authored by Marino Miguel Franzini (1779–1861). This table is included in Almanach Portuguez (Portuguese Almanac) for the year 1826, (Franzini, 1825–1826), the publication of the census performed in Portugal in 1820. Franzini says nothing about the construction of that table or the adaptation made from Duvillard’s table. Franzini is an outstanding figure of the 19th century scientific and social Portuguese scene — naval officer, politician, deputy, member of the

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and benefit tables is recognised to be, ideally, the responsibility of a specialised person, that should study the indeterminacies stemming from the necessary adaptations of mortality tables and the choice of suitable rates of interest — a person with the “profession of Mathematics”; the term actuary was not used: “These details, and all the calculations associated with this delicate matter must be assigned to a person who has the profession of Mathematics because they need a great deal of work and subtlety and rightly we cannot expect from this Board an exclusive dedication to that[...]”.78

Since it was impossible to choose foreign mortality tables to produce actuarial tables which would regulate life assurance coverage, the Board felt that it was only possible to propose survivors’ pension assistance, but using the experience of União de Norwich, the first life assurance company settled in Portugal.79 To accomplish that, the Board felt “forced” to adopt, with minor changes, the survivors’ pension tables of União de Norwich. The benefit table was not changed — a higher profit was expected, since pensions would be paid for a shorter period of time, due to the lower average term of life in Portugal than in England. Contributions should be increased, since they would be received for a shorter period of time and the same capital would be paid. The increment to be applied was a complete “guessing”: “the Board presents, with scepticism, the choice, almost randomly, though just for now [...] of also adopting the pensions defined by the company União de Norwich, but increased by 60 percent”.80

The Board often discussed the possibility of proposing life assurance assistance, but it was only in 1845 that life assurance coverage was proposed; its technical foundations “were, certainly, not much more advanced than the ones suggested in 1836”.81 Resistance from members of Fidelidade to accept this kind of product are documented – in 1846, the financial committee summarised the progress of life assurance coverage as follows:

RASL and president of the first official service of statistics in Portugal, Comissão de Estatística e Cadastro do Reino (Commission of Statistics and Register of the Kingdom), founded in 1815. He was a pioneer in Meteorology and Statistics in Portugal. On Franzini, see (Nunes, 1988). The second of the mentioned texts is Essai statistique sur le Royaumme de Portugal et d’Algarve, (Balbi, 1822), authored by the Italian geographer and statistician Balbi, who spent almost two years in Portugal — the accuracy of the termo medio de vida (average term of life) for the Portuguese population (26,61 years) is questioned, since it was not certain that all deceases were considered. This text provides the first statistical reading of the country, “the best quantitative and qualitative image of contemporary Portugal”, seeking for a comparison with other European countries: (Sousa, 1995, 99). 78 (Companhia de Seguros Fidelidade, 1836, 41). 79 Norwich Union was founded in 1797 in Norwich, in the east of England, as a mutual insurance company with fire coverage and in 1808 life assurance coverage was settled. The first agency settled abroad was in Portugal. An announcement of that company was published in 1824 in Gazeta de Lisboa but it is not clear that other coverage rather than fire was offered: Gazeta de Lisboa 266 (10th November 1824), 1264. The first published plans of União de Norwich date from 1835 — (União de Norwich, 1835) — and survivors’ pensions were offered. Other coverages offered by União de Norwich were life assurance depending on one/two people, life annuities depending on one/two people, retirement pensions and pensions paid to children up to 21 years old. The report made by the Board of Fidelidade raises doubts whether that assistance was actually implemented at União de Norwich — it is only said that Norwich’s tables “have been circulating” — (Companhia de Seguros Fidelidade, 1836, 38). 80 (Companhia de Seguros Fidelidade, 1836, 39–40). The calculations presented for the proposed change of a 60% increase are based on a desired higher profit, supposing, with no evidence, a higher rate of interest (6% rather than 4%) and an average term of life lower than in England (30 years rather than 48). 81 (Alves-Caetano, 2000–2002, I, 75).

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“in this Assembly (we fear) there is a prejudice against this aleatory contract. However, it is less risky than the maritime or the terrestrial, because it is subject to fewer contingencies, and the laws of mortality are better analysed than any other”.82

In 1857, life assurance coverage was officially extinguished in Fidelidade and it was only in the 1920s that a full resumption occurred: low public acceptance of life assurance and successive suspensions motivated by several epidemics crises are mentioned as the main reasons.83 Cláudio Adriano da Costa had the intention of implementing life assurance in Lisbon, on a sound and scientific basis. The obstacles experienced at Fidelidade were probably a reason for proposing another life assurance company. In 1845, he submits the request to found Providência, an assurance company selling life assurance, annuities, survivors’ pensions and reversions, at a time when he was becoming detached from Fidelidade.84 He was the only founding member of Providência. On the activity of Providência, there is not much evidence — it is not certain what the company’s activity was, nor even what insurance coverages were implemented. But it is certain that there was no activity from 1847 onwards and in 1854 the company was liquidated.85 The publication Providência: companhia de Seguros de vida, annuidades, sobrevivencias, reversões, etc. (Providência: Company of Life Assurance, Annuities, Survivors’ Pensions, Reversions, ...) — (Anonymous, 1846) — is a compilation of documents related to the foundation of Providência, where we can identify da Costa’s convictions to submit the proposal of this life assurance company.86 The motivation for da Costa was to contribute to the institution of life assurance — he highlights again the British example and presents his proposal as a novelty in Portugal. Argumentation is focused on the advantages of life assurance for the State. He denounces the huge problem with pensions from retired State employees, and exposes the “incompetence” of the Associação do Montepio das Secretarias do Estado — individuals that planned similar institutions “did not know the precepts prescribed by science”.87 But da Costa also urges the development of private enterprise, to avoid dependence on the State. The popularity and progress of life assurance in the United Kingdom are emphasised while the Portuguese montepios de sobrevivência are doomed to fail: “It should not surprise us that benefit societies like our montepios do not make much profit, they have been condemned abroad for a long time, since everything we rehearse now for the first time was old abroad”.88

Providência offered several coverages: life assurance, term annuities, life term annuities and reversions, regulated by 29 tables which are included in (Anonymous, 1846). The non-existence of Portuguese population’s statistics is once again recognised as a reason for the impossibility of choosing a suitable foreign mortality table to perform premium or benefit tables. There is a reference to English and French mortality 82 (Alves-Caetano, 2000–2002, I, 76). No further explanations are given. 83 (Alves-Caetano, 2000–2002, I, 69–77); (Alves-Caetano, 2000–2002, II, 251–253). 84 Alves-Caetano, António, 1997. Cláudio Adriano da Costa e a Companhia Providência (1845–1854). https://sites.google.com/

site/antonioalvescaetano/home. (Alves-Caetano, 2000) is an adaptation of that text. 85 (Alves-Caetano, 2000, 85). 86 Those documents are: Charter, 28th November 1845, granting da Costa 15 years of exclusivity for the use of his tables; Representations from da Costa to the Queen on the 10th August 1835 and 21st October 1845; “Relatorio” (Report) justifying the importance of the foundation of Providência; “Programma da Companhia Providência” (Programme of the Company Providência); 29 premium tables; “Minuta da Proposta e instrucções para se fazer um seguro de vidas” (Draft of the Proposal and instructions to settle a life assurance); “Estatutos” (Statutes). 87 (Anonymous, 1846, 11). 88 (Anonymous, 1846, 14).

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statistics and mortality tables, but it is not clear which mortality table da Costa used for his calculations.89 Also, it is not clear which statistical data of the Portuguese population was used to produce the tables for Providência.90 Da Costa applied for the exclusivity of the use in Portugal of his tables for 15 years, since they were “the result of much study” and no other assurance company was offering life assurance coverage in Lisbon — “if any company in Lisbon has announced that they operate in life assurance, that is just words”.91 That request was granted to him even though, surprisingly, he did not present the tables in the first place, claiming that they could be intercepted before reaching its destination.92 Da Costa was aware that only science could provide a sound basis for life assurance assistance and knew the difficulties in proposing scientifically based plans. A more detailed investigation on the originality of his contributions, namely calculations used to produce the tables for Providência, is important to determine his role in the progress of actuarial science in Portugal. Until the 1850s, two other Portuguese insurance companies, operating in Porto, included life assurance coverage in their initial statutes but it never came into practice — Garantia, in 1853, only established that assistance in 1920, and in Segurança, founded in 1835, it never functioned.93 Mutual life assurance was the other form of life insurance that was implemented in Portugal during the 19th century, and had wide expression in the 1860s, but we do not explore it in this paper since it is not relevant for actuarial topics. Although our research was focused on the institutions located in Lisbon, it seems that Portuguese life assurance companies did not systematically apply life assurance coverage during the 19th century. They faced the same problems as montepios de sobrevivência with establishing their products on a sound and scientific basis. It was difficult to choose a reliable foreign mortality table to calculate premium and benefit values of life assurance products using life assurance theory, that had been known since the 18th century. Similar difficulties would appear if they chose to use suitable monetary tables which were broadly used by European companies and had also been published since the 18th century (section 1). Besides those technical difficulties, other factors contributed to this scenario — the low acceptance of insurance and a long period of political and economic turmoil — economic and financial crisis in the mid-1840s, and several epidemics in the 1830s, 1840s and 1850s, namely cholera, yellow fever and typhus epidemics, during which new policies were not accepted and old ones were not renewed. Afterwards, there was the domination of foreign mutual life assurance companies. 3.2. The role of the Portuguese government The meetings of the ISC were not significant to the progress of life assurance industry in Portugal during the 19th century — international recommendations to ensure the progress of life assurance companies were 89 The Northampton table is said to be more favourable to insurance companies than the statistical data from Lalande’s Table de

logarithmes. He says that Lalande’s data does not deserve the same trust as those from Northampton’s table, since mortality had not really been much studied by French authors. (Anonymous, 1846, 19–20). 90 The text (Balbi, 1822) is criticised again, for the reference to the average term of life 26,61 years. Statistics concerning a specific group of the population are mentioned — State employees from classes inactivas (inactive classes, or in other words, retired employees). Da Costa was studying a solution to solve problems concerning pension costs with those State employees and five years later he published the text Conversões das classes inactivas (Conversion of the Inactive Classes), (da Costa, 1851). For further information about this topic see (Alves-Caetano, 2000). 91 (Anonymous, 1846, 6). 92 We do not know if those tables were presented later. 93 (Alves, 2005, 201–204). The author refers to the first insurance companies settled in Porto, especially life assurance companies, contextualising it in the economic and social development in Portugal in the 19th century. This text contains a list of foreign insurance companies operating in Porto since the late 1830s — British ones were the first that offered life assurance coverage and in the 1850s and 1860s, Spanish companies also located in Porto.

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not adopted by the Portuguese Government. (We remind the reader that from the 1850s until the early 20th century, Portuguese assurance companies did not offer life assurance coverage — section 3.1.) During the 19th century, two Commercial Codes were published in Portugal but the references to life assurance have no considerations on scientific topics, namely models that could be used by companies or official inspection that should be made. Codigo Commercial Portuguez (Portuguese Commercial Code) — (Borges, 1833)— the first Portuguese law of the kind, sets up insurance activity, in particular maritime trade, but also other coverages, namely life assurance, connected to maritime trade.94 Life assurance is settled with free arbitrage: “It is possible to settle for a fixed term an assurance for one person. Parties choose a fixed fee for the insured items and the specification of all the conditions of the assurance contract is free.”.95

In 1888, another Commercial Code was authorised — (Veiga Beirão, 1888). There is a chapter dedicated to life assurance but there are no considerations on the rules to perform calculations for the different products that were offered: “Life insurance shall comprise all combinations which may be made, by agreement on the delivery of periodic benefits or capital in return of the constitution of an annuity, for life or from a certain age, or even in return of the payment to the insured person, its heirs or representatives or to third parties; and any other similar combinations.”.96

The first law referring explicitly to life assurance coverage with emphasis on mathematical reserves, was set up in the early 20th century, namely in 1907.97 The third chapter, Do funccionamento e da fiscalização das sociedades de seguros (On the functioning and regulation of insurance companies) details the financial organisation of those societies. Special attention is given to mathematical reserves — its constitution, calculation and financial application. There is an explicit intention of comparing the exercise of national and foreign insurance companies settled in Portugal.98 This law also created an official service responsible for the regulation of insurance companies — Conselho de Seguros (Insurance Council), and among its mem-

94 Insurance activity growth in Portugal is closely related to maritime activity and it is only natural that more emphasis to maritime

trade is made in the first Portuguese Commercial Code. A kind of mutual insurance company founded by King D. Dinis (1261–1325) in 1293 in Lisbon claims for Portugal the beginnings of maritime insurance in Europe: (Amzalak, 1917, 13–19). Pedro Santerna, or Pedro de Santarém, eminent Portuguese jurisconsult that lived in the reign of King Manuel I (1469–1521, reigned from 1495 to 1521), is the author of the first book in which the insurance contract was scientifically studied and systematically exposed — Tractatus perutilis et quotidianos de asecuratosnitus et sponsionibus mercatorum (The Very Useful and Daily Treatise on Insurance and on Guarantee for Merchants, 1542): (Amzalak, 1958, 8). Amzalak’s article includes biographic notes about Santerna, a translation to Portuguese of Santerna’s text and a list of the several editions of that text. 95 (Borges, 1833, 282–283). This Code is authored by José Ferreira Borges (1786–1838), jurist, economist and politician. 96 (Veiga Beirão, 1888). (Second book — On special commercial contexts; Title XV — On insurances; Chapter III — On life insurance). The author of this Code is Francisco António Veiga Beirão (1841–1916), professor at the ICIL, lecturer of commercial and maritime law and of international law. 97 Decree-law, 21st October 1907. 98 An entire chapter, chapter VI Das sociedades estrangeiras dos seguros (On foreign insurance companies), would ensure protection of national interests as long as financing conditions were similar — equality in provision of services, protection of insured persons (by government’s supervision) and preservation of national capital in national territory (by restricting, as far as possible, the emigration of gold).

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bers there were professors of accounting and financial operations of the ICIL.99 The possibility of hiring “indispensable experts” was also established to help in the exercise of their functions. This was a very significant change in the regulation of insurance companies and, for life assurance companies, the desired inspection in order to introduce scientific principles in their organisation could be possible. Nevertheless, the success of that law and the efficiency of that Council did not have the desired impact, as in 1929 another regulation, as a remedy for “the disastrous situation which lasted for twenty-one years”, was announced; it was said that “the best part of its goals” was “yet to be accomplished”.100 The reasons for that performance are beyond the scope of this study. 3.3. Notes on the emergence of life assurance industry in the early 20th century The progress of the life assurance industry in Portugal became relevant only in the early 20th century — there was a growing concern with the regulation and supervision of life assurance companies (section 3.2) and with its scientific foundations, which it was thought should be widely disseminated. An illustration of that, a unique initiative of the kind until then, is the publication Bases technicas das companhias portuguezas de seguros de vida: A Nacional, A Lusitana e Portugal Previdente aprovadas pelo Conselho de Seguros e elaboradas pelos seus actuarios (Technical Bases of the Portuguese Life Assurance companies A Nacional, A Lusitana and Portugal Previdente, Approved by the Insurance Council and Produced by Their Actuaries) — (Brederode et al., 1909) — authored by Brederode, Santos Lucas and Pereira da Silva.101 This text is considered as the first “association” of Portuguese actuaries — a cooperation between three actuaries of life assurance companies with the purpose of disseminating its scientific basis.102 The initiative of this publication came from Brederode, considered to be “the first assumed actuary in Portugal”, and its 99 This council should evaluate proposals of new insurance companies, examine their statutes and inspect their bookkeeping,

advise any necessary change on reserve’s plans or premium tables and publish legislation, documents and statistical notes on insurance. On the Insurance Council see (Guerreiro, 2014). 100 Decree-law 17:555, 5th November 1929. 101 In 19 pages, the formulas used to calculate the value of the several products sold by life offices are presented: fórmulas gerais; prémios, reservas e resgastes; seguro misto; seguro de prazo fixo; capital de sobrevivência; renda de sobrevivência; capital diferido; renda vitalícia diferida; seguro combinado (general formulas; premiums, reserves and redemptions; mixed insurance; fixed term insurance; survival capital; survival income; deferred capital; deferred life annuity; combined insurance). Brederode had a Bachelors in Philosophy from the University of Coimbra (the students of the Philosophical Course attended some subjects of the mathematical course). He also attended École des Pont et Chaussées, but we do not have any information on his course of study. He was actuary in several life insurance companies, since 1906; member of the Comité Permanent des Congrès Internationaux d’Actuaires, since 1907; founding member of the Association of Portuguese Actuaries, created in 1926 (general-secretary of the Board); and a member of the Schweizerische Aktuarvereinigung (Swiss Association of Actuaries). Santos Lucas was an Army officer who initiated his academic training at the University of Coimbra. In 1889 he obtained a Bachelors in Mathematics, in 1893 he completed Military Engineering in the Army School and in 1895 he became a Doctor in Mathematics at the University of Coimbra. He was a professor at the Polytechnic School and at the Faculty of Sciences of the University of Lisbon, where he taught mathematical physics, a subject where the teaching of the theory of relativity in Portugal was introduced. In 1908, Santos Lucas became a member of the Comité Permanent des Congrès Internationaux d’Actuaires; in 1926 was a founding member of the Association of Portuguese Actuaries and was nominated president of the Board. He was actuary of several life insurance companies and performed several actuarial studies to reform legislation. For more details, see (Fitas, 2005). Pereira da Silva was also a Doctor in Mathematics at the University of Coimbra and also attended the Army School. He was a lecturer at the Faculty of Mathematics of the University of Coimbra (differential and integral calculus and celestial mechanics) and at the Escola Normal Superior (Higher Normal School) (methodology of mathematical sciences and history of pedagogy). He became a member of the Comité Permanent des Congrès Internationaux d’Actuaires in 1909 and was a founding member of the Association of Portuguese Actuaries. His contributions to science were in history of astronomy, nautical science and Descobrimentos Portugueses (Portuguese Discoveries). On Pereira da Silva’s contributions to actuarial science, see (Martins, 2018a). 102 (Caeiro and Barroso, 2005, 6). This brochure, with 39 pages, was made for the celebration of the 60th anniversary of the Institute of Portuguese Actuaries. It contains biographic notes about relevant personalities in the progress of actuarial science in

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relevance can be recognised in the official determination, in 1934, that every life assurance company should adopt those rules.103 The scientific relevance of this text has not been studied yet. Brederode is a crucial figure in the development of the life assurance industry in Portugal in the early decades of the 20th century. He is distinguished as the founder of the first actuarially-based Portuguese life assurance company, A Nacional, created in 1906; as actuary of several other Portuguese life offices; member of the Insurance Council; editor of publications on life assurance promotion; and author of technical texts on life assurance themes. He also stood out for his interest in actuarial education in Portugal (appendix B) and for his participation at the International Congress of Actuaries. Santos Lucas and Pereira da Silva are also relevant personalities on the actuarial scene in Portugal in the same period — the first, “one of the pioneers of actuarial science in Portugal”; the other with a short passage by the Portuguese actuarial scene, but showing “deep knowledge and acute intelligence”.104 The contributions of these three eminent men to actuarial science have not yet been studied. These three scholars also contributed to the beginning of Portuguese actuaries’ organisation — they were founding members of the first Portuguese professional association of actuaries, created in 1926, Associação dos Actuários Portugueses (Association of Portuguese Actuaries) (appendix C). Despite its short existence, until the current Instituto dos Actuários Portugueses (Institute of Portuguese Actuaries) was founded in 1945, the need for association and affiliation is evident for scholars and actuaries. The possibility of being a section of a mathematical society is suggested by documents from the 1930s. That project took place in 1940 at the Sociedade Portuguesa de Matemática (Portuguese Mathematical Society) — the Permanent Committee of Applied Mathematics should include a “specialist” on actuarial calculus. The first attempts at an association of Portuguese actuaries date from the 1920s, nearly eighty years after the pioneer Institute of Actuaries, created in London in 1848. In Continental Europe, Germany was the first to create an association of actuaries, in the 1860s. After a number of countries in Central Europe, Western Europe and Northern Europe, professional associations of actuaries were founded in Southern Europe, namely in Spain and Portugal.105 4. Concluding remarks This paper is an introduction to and an overview of the history of actuarial calculus in Portugal until the late 19th century, on which too little is known, with focus on survivors’ assistance provided at montepios de sobrevivência, founded in the late 18th century with a mutualist character, and life assurance companies, which were created with mercantilist purposes in the 1830s and 1840s. Life annuity theory and life assurance theory were established in the mid-18th century and several English and French texts could be used to perform actuarially sound survivors’ pension schemes or life assurance schemes by users who had a reasonable mathematical knowledge. Societies providing survivors’ pensions and life assurance were established in Europe in the second half of the 18th century, some of them based on scientific foundations. The few texts on actuarial topics written by Portuguese authors before the late 19th century show that actuarial science was not a common field of research for Portuguese scholars — six texts, written by three authors, Claúdio Adriano da Costa, Daniel da Silva and Marrecas Ferreira. Portugal who were members of that society and reproduction of important documents related with this professional association of actuaries. 103 (Caeiro and Barroso, 2005, 6); Circular n.o 128, 5th June 1934. 104 Anonymous, 1926. Eleições. Seguros e Finanças 2.a série, n.o 6, 49–50; (Brederode, 1926). 105 There seems to be some coincidences between actuarial activity in Portugal and in Spain — an important regulation of the life assurance industry in the early 20th century (in Portugal, in 1907; in Spain, in 1908), the foundation of professional associations of actuaries in the 1920s (in Portugal, in 1926; in Spain, in 1927) and the current associations founded in the 1940s (in Spain, in 1942; in Portugal, in 1945). The study of the cooperation between Portuguese and Spanish actuaries is a topic beyond the scope of this paper.

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(Also, a translation of a French treatise, made by Dantas Pereira.) These contributions show that life assistance was considered an important topic for the progress of the Portuguese society and reveal the interest in promoting it and disseminating its scientific principles, mainly by people who were connected to societies providing that assistance. During the 19th century, pension funds created at Portuguese montepios de sobrevivência were not scientifically based. Significant changes were not made on pension attribution rules and associations that did not go bankrupt, had to look for solutions to mitigate financial problems. As for life assurance, it is not clear which foundations were used to found the only significant life assurance company, even though it was liquidated in the late 1850s. Until the 1870s, there were no conditions for Portuguese institutions to produce actuarially sound pension schemes or life assurance schemes. In fact, statistics about the Portuguese population, namely mortality statistics, only became reliable in the 1860s, collected under the guidelines of the International Statistical Congress and that enabled comparisons of the Portuguese population. It was not possible to choose foreign mortality tables to produce actuarial tables using life annuity or life assurance theories or to choose reasonable monetary tables broadly used by European institutions. A comparative study of the Portuguese population to guide in that choice was only published in the 1870s, but its use by the most part of the montepios de sobrevivência was limited — each association should have been able to characterise their group of associate members but most did not have regular statistical data procedures. In other countries, general statistics of population were used to produce actuarial tables before particular statistics of societies were published. In the United Kingdom, local burial, baptism records and records of government annuitants for a particular period were used before statistics were collected in the 1830s/1840s (for friendly societies), in the 1840s (for life assurance assistance) and in the 1860s (for widows’ funds). In France, Déparcieux’s mortality table, widely used until the late 19th century, was also produced from records of government annuitants; the first statistics of mutual benefit societies were published in the 1850s and for life assurance companies only in the 1890s. In Portugal, statistical investigations of the population were performed early from the 15th century but we found no evidence of its use to produce pension plans or life assurance products before the 1860s, when statistical data have become credible. The statistical data from montepios de sobrevivência collected in national inquiries during the second half of the 19th century was not used to construct mortality tables but there is evidence of the use of data collections of a few montepios to adjust its pension plans. The first contributions to the construction of Portuguese mortality tables were made in the 1940s. The unscientific pension attribution rules used at montepios de sobrevivência, where contribution and benefit calculations were not based on the ages of the member and of the beneficiary, lasted throughout the entire 19th century. We have found no evidence of a Portuguese model that could have been used. The difficulty of defining the initial plans established at the Portuguese montepios de sobrevivência is similar to what happened at foreign societies, namely at Scottish widows’ funds — shrewd far-seeing men, animated by a noble benevolence, who managed to equate the revenues and expenses when they had no statistical data about the association’s members. The foundation and progress of Portuguese montepios de sobrevivência up to the late 19th century had similar problems as British and French institutions that provided survivors’ pensions — the absence of statistical data about its members, the difficulty of defining pension plans that observed actuarial principles and the mistrust of specialists about actuarial decisions. The study of the most prosperous of the Portuguese montepios de sobrevivência, Montepio Geral, which served as an example for other associations, namely by the adoption of its tables, highlights several topics concerning the progress of those mutual benefit societies: financial difficulties and discussions around the viability of its pension fund; studies performed by members and the use of scientific methods; reception and impact of those contributions. Although it is a single case, the study of Montepio Geral shows that the scholars who performed those studies were also noticed for other activities that were relevant for the progress of montepios de sobrevivência in general — as members of the commission that studied all the associations

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of the country, in the 1860s, in teaching or in professional associations of actuaries. Montepio Geral had among its members individuals with the intellectual potential to study problems related to the viability of its pension plan, namely professors at institutions of higher education and members of the Royal Academy of Sciences of Lisbon. An actuarial department was founded only in 1917; meanwhile, the services of mathematicians are documented — in the 1860s (Daniel da Silva), and from the 1880s until the 1920s, besides mathematicians (Santos Lucas and Caraça, who were also actuaries), the majority were professors at the industrial and commercial institutes where actuarial education begun in the late 1880s (Marrecas Ferreira, Prazeres and Beirão da Veiga). The activities of those scholars and the topics that were taught at those institutes suggest the intention of approximating actuarial instruction to the practice of institutions where graduates in commerce would perform the duties of actuaries, namely at montepios de sobrevivência. All of them were aware of the incorrect foundational principles of pension funds of Portuguese montepios de sobrevivência, and they knew about the progress of foreign institutions and the theoretical background necessary to produce actuarially sound pension plans. Nevertheless, the contributions they gave minimised the consequences of the complex and unscientific organisation of the pension plan settled at the Montepio Geral. The Portuguese government did not completely fulfil its role as a regulating and supervising authority of montepios — until the 1890s, those associations developed with no regulation, particularly montepios de sobrevivência. In England and France, the delay in regulation of those kinds of societies was not so great, but the acceptance of regulatory procedures was also a difficult process — in England, the first societies were created in the mid-18th century and the first regulation was approved in the 1790s; in France, similar societies were founded in the late 18th century and its first regulatory act was approved in the mid-19th century. The consequence of such difficulties was also observed in the guaranty of correct scientific foundations for those societies. As for life assurance assistance in Portugal, evidence shows that in the 19th century only one person stands out, Cláudio Adriano da Costa, associated to the only two companies founded in 1835 and 1845. Although those companies were liquidated in the 1850s, the scientific relevance of da Costa’s contributions must be clarified. The Portuguese government did not promote the progress of institutions — even though the first regulation in the insurance industry dates from the 1830s, it was only in the early 20th century that type of legislation explicitly mentioned the scientific organisation of life assurance companies. Life assurance coverage was not systematically applied during the 19th century, similarly to what happened, for instance, in France. The life assurance industry was not relevant in Portugal before 1907, when a new regulation of the insurance business was promulgated — similarly as in France, where a regulatory act was approved in 1905. This paper highlights the context for research on several topics of the history of actuarial calculus in Portugal. It is imperative to evaluate the contributions of several scholars. Some were motivated by corporative links to montepios de sobrevivência or life assurance companies, aiming at the solution of problems related with the economic sustainability of those institutions. Several excelled not only in studies within institutions, but also in teaching or in involvement in professional associations. Respecting the most relevant, we identified two categories — some of them had no specific academic training on actuarial mathematics but mobilised their intellectual skills for the study of themes on life assurance and survivorship pensions — Cláudio Adriano da Costa, Daniel da Silva, Brederode, Santos Lucas and Pereira da Silva. Others, were teachers at institutions of higher education and their activity on montepios de sobrevivência or life assurance companies shows a connection between theory and praxis — Marrecas Ferreira, Prazeres, Beirão da Veiga and Caraça. In the early 20th century there was an intense activity to promote the scientific progress of life assurance industry and Brederode is unquestionably a leading figure. Concerns on regulation, instruction and association are key issues until the 1940s. It is necessary to study the progress of actuarial education in Portugal, which began in the third quarter of the 19th century, at the Industrial and Commercial Institute

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of Lisbon and the Industrial and Commercial Institute of Porto, but was considered unsatisfactory until the 1940s, at least in Lisbon. It is essential, for instance, to study the activity of the Centre of Mathematical Studies applied to Economics and determine its relevance to the improvement on actuarial instruction. The detailed study of the academic training provided at the industrial and commercial institutes will allow the characterisation of the actuary profession and contextualise the presence of individuals with a great variety of academic qualifications in the institutions’ staff — montepios de sobrevivência, life assurance companies and banks. In particular, since, in the mid-20th century, the actuarial profession was usually performed by those who had graduated from a department of mathematics, it is relevant to study an actuary’s professional career, namely the transition from a theoretical academic training to the exercise of a profession that required the mobilisation of mathematical knowledge in several areas of mathematics and also economics. The study of the professionalisation of actuaries in Portugal must necessarily evaluate the activity of the Association of Portuguese Actuaries, the first professional association of actuaries, founded in 1926 and extinguished somewhere in the mid-1930s. Before the current Institute of Portuguese Actuaries was founded, in 1945, actuaries tried other forms of association — the connection of actuaries to the Portuguese Mathematical Society, between 1940 and 1945, reinforces the existence of a close relationship between the community of mathematicians and the community of actuaries, which needs to be enlightened. Acknowledgments We thank the referees for their comments on an earlier version of this paper, which allowed for considerable improvements. The research for this paper was supported by Fundação para a Ciência e a Tecnologia, I.P., through the Project: UID/HIS/00286/2019.

Appendix A. Notes on the impact of the International Statistical Congress on practices in Portugal in the second half of the 19th century From the point of view of the development of statistics in Portugal, in the mid-19th century Portugal was living the statistical stage, when official services functioned according to international standards, introduced by the International Statistical Congress (ISC): “The institutionalization of Statistics emerges as one of the pillars of the Modern State, not only at the service of political power, but also of civil society, as a centre to collect and process statistical data that systematically allowed one to learn about the state of the Nation or to analyse particular aspects from demography to social facilities and economic dynamics.”.106

Fontes Pereira de Melo, Minister of Public Works, Commerce and Industry, and one of the major players of the Regeneration period, put into practice an extensive programme of economic reform in several fields such as agriculture, commerce, industry and education. The foundation of the Ministério das Obras Públicas, Comércio e Indústria (Ministry of Public Works, Commerce and Industry) in 1852, a super-ministry where several statistical sections were formed in the Departments of Agriculture, Commerce and Manufactures, is an example of the Government’s agenda, showing concerns about the institutionalisation of statistics. The ISC was founded in the mid-19th century with the main purpose of setting up the foundations of a general statistic, as a corpus, universal for all nations, in order to make possible a comparison of the progress 106 (Sousa, 1995, 19). This text is a history of Portuguese official services founded in the 19th century that made possible the

gathering of public, official and private statistics. It contains digitalisations/transcriptions of several relevant documents.

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of nations. For a quarter of a century, the ISC met in different European cities — Brussels (1853), Paris (1855), Vienna (1857), London (1860), Berlin (1863), Florence (1867), The Hague (1869), St. Petersburg (1872) and Budapest (1876).107 The importance of the sessions of the ISC to actuarial practice can be recognised in the assiduous presence of members of the Institute of Actuaries and in the reports published in The Assurance Magazine and Journal of the Institute of Actuaries. Portugal was not always represented in the ISC meetings: in a total of nine meetings it was represented in six (the 1st, 2nd, 5th, 6th, 8th and 9th), by politicians, ministers, professors of the University of Coimbra, members of the Academia Real das Ciências de Lisboa (Royal Academy of Sciences of Lisbon, RASL) and people responsible for official statistical services.108 Only two of the Portuguese reports of the ISC meetings were published, (Ávila, 1854) and (Ávila, 1864), referring to the meetings held in Brussels and Berlin. Approximately one hundred publications in the Portuguese language were offered, mostly official reports from the period 1855–1869; but in the Budapest’s meeting (1876) it was said that the progress of statistics in Portugal was unknown because the publications offered were more than a decade old.109 During the second half of the 19th century, the Portuguese government intended to follow the international guidelines of the ISC to learn more about the state of the Nation, which was in accordance with the agenda of the political movement of Regeneration. Particularly on statistical data of the population, census had been conducted in Portugal since the mid-15th century but the first population census according to the international guidelines of the ISC only happened in 1864.110 The rel107 Despite the fruitful collaboration between the main statisticians, the meetings of the ISC did not occur continuously and there

was not much consistency in the participants from the different countries either. However, international cooperation continued and, in 1885, the International Statistical Institute was founded, continuing the project of the ISC. 108 In Brussels, Ávila; in Paris, Ávila, Matias de Carvalho e Vasconcelos (1832–1910) and Sebastião José de Ribeiro e Sá (1822–1865); in Berlin, Ávila and Vasconcelos; in Florence, José de Torres (1827–1908); in St. Petersburg, Frederico Francisco Stuart de Figanière e Morão (1827–1908); and in Budapest, Vasconcelos. Ávila was a conservative politician of the Constitutional Monarchy. He had a Bachelors in Philosophy from the University of Coimbra. He was a deputy and minister for several years, peer of the Realm, State councillor, civil governor and diplomat, member of the RASL, count (1864), marquis (1870) and duke of Ávila e Bolama (1878). Vasconcelos had a Bachelors in Mathematics and was a Doctor in Philosophy from the University of Coimbra; a lecturer at the Faculty of Philosophy of the same university. In 1859, he became responsible for a scientific commission ordered by the Portuguese Government. That possibly explains his nomination to represent Portugal at the meeting in Berlin in 1863. Ribeiro e Sá was Chief of the Manufactures Department of the Ministry of Public Works, Commerce and Industry. José de Torres was known for his contributions in the development of statistics in Portugal — he became responsible for the Repartição Central de Estatística (Central Statistical Bureau), created in 1859, for almost half a century, until his death. His interest in statistics began in 1857, and in 1859 he undertook a trip, at his own expenses, to France, England, Germany and Spain, in order to improve his knowledge in that area. Viscount Figanière was a diplomat, writer, historian, poet and philosopher, member of several societies, including the Instituto Histórico e Geográfico do Rio de Janeiro (Historical and Geographical Institute of Rio de Janeiro), RASL, Instituto de Coimbra (Coimbra Institute) and Associação de Arquitectos e Arqueólogos (Association of Architects and Archaeologists). From 1870 to 1876 he was minister plenipotentiary in Russia and we believe that was the reason why he was present at the session in St. Petersburg. 109 For more details see (Martins, 2012, 242–248). We assume that these critics refer to the antiquity of the texts, mostly from the 1850s and 1860s. 110 From the mid-15th century, a few population assessments had been performed but without scientific purposes, rather with military or tax purposes. Referring to the censuses performed in Portugal in the first half of the 19th century, Tiago Oliveira (1928–1992) says they were “more like a reasonable imitation of what happened in Europe than a conscious and integrated rational need”, since there were no concrete resolutions after it — (Oliveira, 1980, 29). In this text, Tiago Oliveira stresses the inaccuracy of the Portuguese population’s statistics collected from the mid-15th century. He was a recognised mathematician and university professor who became known in the resistance against the Ditadura Nacional, the political regime that ruled in Portugal from 1926 until 1974. His area of interest was statistics, namely in investigation and teaching. He was one of the founders of the Centro de Estatística e Aplicações (Center of Statistics and Applications) of the Faculty of Sciences of the University of Lisbon, in 1975, and of the Sociedade Portuguesa de Estatística (Portuguese Statisti-

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evance of that achievement for actuarial practices was massive and that was acknowledged by scholars. Despite the initiatives of the Portuguese government, the different official statistical services founded during the second half of the 19th century were frequently criticised. A study of the reasons for its inefficiency are beyond the scope of this paper. The international recommendation that every country should establish a Central Statistical Commission, or a similar office, was made in the first meeting of the ISC, in 1853. In Portugal, the Comissão Central de Estatística do Reino (Central Statistical Commission of the Kingdom) was established in 1857, with the purpose of organising a general plan for statistics in all the departments of public administration. Its inefficiency was recognised in 1859, when another official service was created, the Repartição Central de Estatística (Central Statistical Office) — being a commission, it had a transitory nature and therefore its results were meagre; in 1859 a “more stable and institutionalised service” was chosen.111 José de Torres was in charge of the Central Statistical Commission and the efficiency of this other service was also questioned when the Conselho Geral de Estatística (General Statistical Council) was founded in 1864 — it was necessary “to overcome a scenario characterised by isolated and unconnected works, with gaps, duplications and absurdities”.112 This Council was formed with the intention of defining clear goals and principles for statistical inquiries, which were meant to be coordinated by a single service.113 Given its inefficiency, failing the purpose of unifying and bringing order and unity to statistical services, in 1869 the Comissão Central de Estatística (Central Statistical Commission) was created.114 Finally, in 1887, the Conselho Superior de Estatística (Superior Statistical Council) was formed towards further specialisation and the principle of statistical authority was set up.115 Official statistics services created during the second half of the 19th century in Portugal were based in a “model of decentralised competencies”, in which statistical data was provided by different official services, making it inefficient: “The result is that the collection of data becomes a goodwill between institutions and people”.116 The RASL, founded in 1779, had a very important role in the development of Portuguese mathematics in the 19th century.117 The involvement of the RASL on the development of statistics, considered at those times as an experimental method applied to moral, economical and political sciences, particularly concerning the ISC, was basically reduced to the participation of official delegates. We found no references to the ISC meetings from 1852 to 1869 (the most relevant period for the progress of mutual benefit societies and life assurance companies) neither in the minutes books of the sessions of the 2.a Classe de Ciências Morais e Políticas e Belas Artes (Second Class of Moral and Political Sciences and Belles Lettres), of the 1.a Classe de Ciências Matemáticas, Físicas e Naturais (First Class of Mathematical, Physical and Natural cal Society) in the early 1980s. On Tiago Oliveira, see Reis, Fernando. n.d. José Tiago da Fonseca Oliveira (1928–1992). http:// cvc.instituto-camoes.pt/ciencia/p40.html. 111 (Sousa, 1995, 149). 112 (Sousa, 1995, 151). 113 In 1866 eleven sections were organised: Territory, Population, Industry, Civil Administration, Public Health, Public Beneficence, Public Instruction, Ecclesiastic Administration, Court Receivership, Financial Administration and Military Administration. 114 Decree-law, 16th December 1869. 115 (Sousa, 1995, 155). 116 (Madureira, 2006, 90–93). In this text, the author discusses a history of changes in thinking and social movements, in governmental politics and practices, using the progress of calculus and statistics as connecting themes. 117 Until the mid-19th century, the only journal in Portugal where mathematical texts could be published were the Memórias da Academia Real das Ciências de Lisboa (Memoirs of the Royal Academy of Sciences of Lisbon) of the RASL; from 1866 until 1923, the Jornal das Sciencias Mathematicas, Physicas e Naturaes (Journal of Mathematical, Physical and Natural Sciences), also of the RASL, was regularly published; and from 1851 until 1923, a Bulletin including the proceedings of the RASL public sessions was also published. On the mathematical sciences’ publications of the RASL, see (Rodrigues, 2004). On the mathematics in the publication Memoirs of the RASL, see (Saraiva, 2008).

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Sciences), nor in the Memórias da Academia Real das Ciências de Lisboa (Memoirs of the Royal Academy of Sciences of Lisbon).118 We emphasise that, from the five Portuguese delegates to the ISC, only one was not an academician, Sebastião José de Ribeiro. The reasons for that lack of engagement are beyond the scope of this study. Nevertheless, even before the ISC meetings began, in the RASL the performance of a statistical inquiry to the Nation was proposed. The initiative, presented in March of 1852, came from the historian Alexandre Herculano (1810–1877), a member of the Second Class of Moral and Political Sciences and Belles Lettres and one of the inspiring sources of the Regeneration period, which he prepared ideologically. He argued about the relevance of such a study and suggested that instructions and questionnaires should be defined “in harmony with the progress of science”, in order to receive permission from the Government to perform such an inquiry and study the data collection; he aimed: “to publish in regular periods of time, if not a complete statistic of the country [...] at least a study that is sufficient to solve economic problems and to clarify lawmakers about the laws related with general statistics”.119

António Oliveira Marreca (1805–1899) was the academic nominated to study the feasibility of that project and in June of 1853 the report Parecer e Memoria sobre um projecto de Estadistica (Report and Memoir on a Project of Statistics) — (Oliveira Marreca, 1854) — was published.120 That publication occurred after the first meeting of the ISC, in September of 1853, and it is only natural that Marreca referred to it in order to justify some measures suggested by him, namely the constitution of local commissions. There is a difference in what should be the RASL intervention — to choose the academics and provincial associates to whom should be sent statistical inquiries — and the State cooperation — to coordinate the services under its responsibility, allowing the RASL to collect statistical data about population, agriculture, industry and internal trade. This project was initiated in 1855 — instructions were given to correspondent members of the RASL in order to nominate statistical commissions121 and from then on, we find, in the minute’s books of the Second Class sessions, references to correspondent members responsible for that statistical collection. We did not investigate the effectiveness of the implementation of this initiative of the RASL. Marreca had the intention of continuing that project, focusing on economical and moral issues, but that did not happen.122

118 For more details on the development of statistics in the 19th century and the RASL, see (Martins, 2012, 489–493). The Second

Class was the most related with statistics, namely the Secção de Ciências Económicas e Administrativas (Section of Economical and Administrative Sciences). The First Class could be relevant for our purpose of studying the influence of the RASL in the development of statistics in Portugal because Daniel da Silva, a mathematician who made some contributions in actuarial calculus, was a member of that Class and wrote a paper about the Portuguese populations’ statistics, particularly mortality statistics, (da Silva, 1869), published in the Journal of Mathematical, Physical and Natural Sciences of the RASL (section 2.3). 119 Academia das Ciências de Lisboa, Sessões litterarias de Novembro de 1844 a 17 de Junho de 1852 — Book 40B of the Academy’s Secretariat, 26-03-1852. Herculano was a Portuguese poet, historian, journalist, politician and novelist, one of the writers who is credited for introducing Romanticism to Portugal. 120 Oliveira Marreca was a multifaceted person — historical novelist, publicist, animator in clubs of intellectuals, professor, public services administrator and a political and economic leader. He was appointed professor of Political Economy at the Instituto Industrial de Lisboa (Industrial Institute of Lisbon) when it was founded in 1852 and was a member of the RASL. In politics, he was a deputy from 1838 until 1858. On Oliveira Marreca, see (Bastien and Campos, 2005). 121 Academia das Ciências de Lisboa, Sessões litterarias — Book 21B of the Academy’s Secretariat, 25-01-1855. 122 (da Silva, 1858–1923, XXII (1923), 334).

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Table B.1 Curso Superior de Comércio at ICIL — subjects on mathematics, commercial accounting and actuarial mathematics (1888). 1st year, preparatory course 4th subject (Arithmetic, Algebra, Synthetic Geometry) 2nd year 6th subject (Plan Trigonometry, Principles of Geometry, Superior Algebra, Infinitesimal Calculus) (requires the 4th subject) 3rd year 22nd subject (General Accounting and Commercial Operations) (requires the 4th subject) 4th year practice of the 22nd subject 5th year 28th subject (Financial Operations) (requires the 6th and 22nd subjects)

Appendix B. Notes on actuarial education in Portugal (1884–1949) Instruction in actuarial mathematics began in Portugal in the last quarter of the 19th century, in Lisbon and Porto, at the Instituto Industrial e Comercial de Lisboa (Industrial and Commercial Institute of Lisbon, ICIL) and the Instituto Industrial e Comercial do Porto (Industrial and Commercial Institute of Porto, ICIP).123 We will only refer to the instruction at the ICIL. The analysis we made is mostly descriptive, focused on programmes of the different subjects and legislation. The Curso Superior de Comércio (Higher Course in Commerce) was a five-year technical-professional course, created in 1884 in the ICIL but only in 1888 received a regulation.124 In Table B.1, we list the subjects in mathematical commercial accounting and actuarial mathematics. Two subjects on mathematics are included: in the first year, the 4th (Arithmetic, Algebra, Synthetic Geometry) and, in the second year, the 6th (Plan Trigonometry, Principles of Geometry, Superior Algebra, Infinitesimal Calculus), that required the 4th. The 28th subject (Financial Operations) is the most relevant for our purpose. Taught in the fifth year, it became a biannual subject in 1898, taught in the fourth and fifth years of the curriculum.125 It had the precedence of the 6th subject and the 22nd subject (General Accounting and Commercial Operations). In the fifth year, there were also visits to different kinds of institutions, namely Customs and Commercial Establishments. The programme of the 28th subject, (Instituto Industrial e Comercial de Lisboa, 1888, 159–165), is authored by Marrecas Ferreira, nominated its teacher in 1886. It includes themes of financial calculus, probability calculus, annuities, life assurance, life term annuities, topics on saving banks and montepios. The importance given to the study of the conditions of financial stability in montepios and high-risk banking operations, suggests the intention of providing training to individuals who performed functions of actuaries at montepios de sobrevivência, life assurance companies or banks. Concerning montepios de sobrevivência, this programme includes the title Pensões de sobrevivência nas associações do tipo do Montepio Geral (Survivorship pensions on associations like Montepio Geral), with topics that have a close correspondence with the dissertation of Marrecas Ferreira, elaborated for the position of Full Professor of the 28th subject, Estudo sobre monte-pios — (Marrecas Ferreira, 1886) — (section 2.3), namely respecting the construction of tables, calculation of fees and mathematical reserves. 123 ICIL and ICIP were founded in 1869, when industrial and commercial instruction was organised in Portugal. Their predecessor

schools were Industrial Institute of Lisbon and Escola Industrial do Porto (Industrial School of Porto), created in 1852 with the purpose of offering industrial instruction. For more details on actuarial education in Portugal, from 1884 until 1949 see (Martins, 2012, 510–558). 124 Pre-requisites for the course included a Portuguese language exam similar to that given for admission in high-schools. In mathematics, the evaluated topics were arithmetic, elementary geometry and its most usual applications. 125 We suppose that the extension of its programme justified that change as the initial programme was basically divided in two.

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In 1911, the ICIL was divided into two schools — the Instituto Superior de Comércio (Higher Institute of Commerce, HIC) and the Instituto Superior Técnico (Higher Technical Institute). The Higher Course in Commerce, taught at the HIC, became a course of higher education but despite a new curricular organisation, actuarial topics were very similar to the ones taught at the ICIL.126 That course maintained its designation until 1927, when it was renamed as Curso de Finanças (Finance Course). Inspection of subjects’ programmes seem to make it evident it that the actuarial topics taught at the ICIL during the periods 1886–1891 and 1893–1911, and at the HIC, at least until 1919, were the same. In the 1910s, there was a proposal to introduce actuarial education at the University of Coimbra, but with no success. When the Faculty of Sciences of that university, created in 1911, was being organised, the vice-dean and professor at the same school, Sidónio Pais (1872–1918), proposed the inclusion of a course on insurance mathematics (and another one on statistics) in the mathematical sciences’ section of that Faculty.127 His proposal was not accepted because some professors did not consider that topic appropriate to be included at a university. In 1930, the Universidade Técnica de Lisboa (Technical University of Lisbon) was founded and in 1931 the HIC was integrated in it and was renamed as Instituto Superior de Ciências Económicas e Financeiras (Higher Institute of Economic and Financial Sciences, HIEFS). This was the first institution of higher education where a subject with the designation Cálculo Actuarial (Actuarial Calculus) was taught, in the fourth and last year of the Curso Superior de Ciências Económicas e Financeiras (Higher Course in Economical and Financial Sciences). In 1938, it was recognised that actuarial instruction given at the HIEFS did not reflect the development of important areas such as mathematical statistics, probability and its applications to life assurance industry and mathematical theory of financial operations, crucial topics for exercising the professions for which its graduates would be qualified. The solution found by some professors was the foundation of a research centre, the Centro de Estudos de Matemáticas Aplicadas à Economia (Center of Mathematical Studies Applied to Economics, CMSE).128 Bento de Jesus Caraça presented the proposal for that research centre to the Conselho Escolar (Scholar Council) of the HIEFS in January 1938 and it was underwritten by Beirão da Veiga and Aureliano de Mira Fernandes. Caraça was the person responsible for the management of the CMSE’s activities. Three sections were considered — Actuarial Calculus, Applied Statistics and Mathematical Economics.129 The intention of offering a more solid academic background to future actuaries was a failed project; the CMSE was extinguished in 1946 by ministerial decision, possibly because of Caraças’ political activity.130 There is no study on the activity of CMSE or on the activities of Caraça, Beirão da Veiga and Mira Fernandes on actuarial calculus.

126 There is a correspondence between the themes taught in the 28th biannual subject (Financial Operations), at the ICIL, taught in

the fifth year, with two subjects taught at the HIC, in the 4th and the 5th years, the 20th (Long Term Financial Operations) and the 21st (Insurance, Welfare Institutions, Insurance Accounting), respectively — (Instituto Superior de Comércio, 1916a) (Programme of the 20th subject); (Instituto Superior de Comércio, 1916b) (Programme of the 21st subject). 127 (Pereira da Silva, 1912, 13). This letter shows the interest of Pereira da Silva and Brederode in the progress of actuarial education in Portugal. It is addressed to Brederode as a response to a request that he made to Pereira da Silva to check the instruction given at German universities, during a stay in Berlin. 128 (Beirão da Veiga et al., 1938). On CMSE, see (Bastien, 2010, 19–30) and (Morgado, 1995, 14–15, 42–43). (Bastien, 2010) contains a compilation of unpublished texts of Caraça, which show the convergence of his social and scientific interests. 129 This proposal established three main activities for CMSE: conferences and lectures, organisation of individual and collective works; publication of works from its collaborators; and promotion of relationships with similar foreign organisations. 130 Disciplinary proceedings were opened in 1946 against Caraça by the Ministry of Education because he had signed a manifesto against the admission of Portugal in the United Nations. As a result of this process he was expelled from the HIEFS and was prohibited to teach in any public or private school. In the same year he was arrested by the political police Polícia Internacional e de Defesa do Estado (PIDE — International Police and State Defence).

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With the first reform of the HIEFS, in 1949, the similarity between the courses taught and the ones of the predecessor institutions continued and that was severely criticised: “for more than thirty years, the organisation of the Institute has not undergone substantial changes”.131

In the 1950s, actuarial mathematics continued to be taught at the HIEFS, but in the 1970s and 1980s, a decline was observed.132 There were only three professors of actuarial mathematics from the first reform of the ICIL (1888) until the establishment of HIEFS (1930), emphasising the continuity of those institutions — Marrecas Ferreira, who taught from 1888 until 1923, Prazeres, teaching from 1893 until 1922 (he died in 1922) and Beirão da Veiga, who began his career as a teacher in 1908.133 The activities of those professors reveal the relationship between praxis and theory, which was recognised to be important. In the mid-20th century, at the 14th International Congress of Actuaries it was stated that, in Portugal, the exercise of the profession of actuary was performed by those who had graduated in Mathematics from the Universities of Coimbra, Porto and Lisbon, graduated in the course of Ciências Económicas e Financeiras (Economical and Financial Sciences) of the Universidade Técnica de Lisboa and others who had studied actuarial science on its own.134 Appendix C. Notes on Portuguese professional associations of actuaries (1926–1945) The first Portuguese professional association of actuaries was founded in 1926, the Associação dos Actuários Portugueses (Association of Portuguese Actuaries, APA), an association of which we know little about but that by 1936 had already been dissolved.135 The Border of APA was composed by three actuaries — Santos Lucas, president of the Board, Beirão da Veiga, its vice-president, and Brederode, its generalsecretary. The aim of APA was to promote the “progress and diffusion of actuarial science and protect the interests of the Portuguese actuaries”, defining seven measures to achieve it; the fifth shows that in the 1920s some companies did not have scientific foundations: “To strive in Portugal for the adoption of scientific methods in the organisation and functioning of welfare institutions.”.136

Eighteen of the twenty one founding members of APA are identified as being or having been actuaries — seven graduated from the Course on Commerce at the ICIL or HIC and six graduated in Mathematics (two Doctors from the University of Coimbra and the other four completed their degrees at the University 131 Law, 17th October 1949 (Portaria). 132 In 1972, the HIEFS became known as Instituto Superior de Economia (Higher Institute of Economics) and in 1990, as the cur-

rent Instituto Superior de Economia e Gestão (Higher Institute of Economics and Management). In the 1990s, the latter institution became a pioneer in post-graduated training in actuarial science, which training continues to the present day. 133 Marrecas taught at the ICIL these subjects: Financial Operations; Superior Algebra, Analytic Geometry, Infinitesimal Calculus; at the HIC, Infinitesimal Calculus and Probability Calculus; Statistics. Prazeres, taught at the ICIL these subjects: Accounting and Commercial Operations; Calculus of Financial Operations; at the HIC, Financial Operations; Insurances, Providence Institutions, Insurance Accounting. Beirão da Veiga taught at the ICIL and at the HIC the same subjects as Prazeres, as an assistant professor, and at the HIEFS, Financial Operations; Actuarial Calculus. 134 (Beirão da Veiga and Martins, 1954). 135 See (Queiroz de Barros, 1936). The author mentions that APA had a “short” existence but does not explain the reasons for that. In this article, the author stresses the lack of regulation for the actuary profession — on the one hand, the difficulty of life assurance companies to hire qualified professionals and, on the other hand, the obstacles for mathematicians to get a position in those institutions. 136 (Associação dos Actuários Portugueses, 1926).

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of Lisbon).137 As for the exercise of teaching in institutions of higher education, we identify four of them teaching at the HIC (one was a retired professor), two at the Faculty of Sciences of the University of Lisbon, one at the Faculty of Sciences of the University of Coimbra, and one at the Higher Technical Institute. There were also two professors at the Escola Elementar de Comércio de Ferreira Borges (Elementary School of Commerce Ferreira Borges), a secondary school. The contributions of all of them on topics of actuarial science have not yet been studied yet and there is also no study of the APA. The Instituto dos Actuários Portugueses (Institute of Portuguese Actuaries, IPA) was founded in 1945 and it is the current Portuguese association of those professionals. There is a coincidence of several of the founding members of the IPA and of the APA, showing a continuity between the two institutions — Adolphe Moysan, António Maria Pires, Beirão da Veiga, Clotilde Ferreira Rodrigues, João de Matos Rodrigues (1887–1971), Luciano Ribeiro, Octávio da Fonseca Brito, Luís Felipe Leite Pinto and Pedro Teotónio Pereira (1902–1971), representing 43% of the founding members of APA and 12% of the founding members of the IPA.138 Between the extinction of APA and the foundation of IPA, Portuguese actuaries tried other forms of association. In the 1930s, there was the intention of founding a Portuguese society of mathematics, where a special actuarial section would be considered.139 That institution was founded in 1940, the Portuguese Mathematical Society (PMS) and five Comissões Permanentes (Permanent Committees) dedicated to scientific areas, were created — the Applied Mathematical Committee should have a “specialist” on “actuarial calculus”.140 There is no study on the activities of those Permanent Commissions of PMS, namely on actuarial science.141 Among the 78 founding members of the IPA there were 31 (43%) that were also members of the PMS in 1947.142 References Alborn, T., 2009. Regulated Lives: Life Insurance and British Society 1800–1914. University of Toronto Press, Toronto. Almeida, P.T.d., 1995. A construção do Estado Liberal. Elite política e burocracia na Regeneração (unpublished doctoral thesis on political sociology). Faculdade de Ciências Sociais e Humanas da Faculdade de Letras da Universidade Nova de Lisboa, Lisboa, Portugal. Almeida, T.M., 2018. Biografia de José Maria Dantas Pereira (unpublished master’s thesis on military naval sciences). Escola Naval, Alfeite, Portugal. 137 Adolphe Moysan, António Maria Pires, António dos Santos Lucas, António dos Santos Viegas, António Soriano Mendes Lage,

Caetano Maria Beirão da Veiga, Clotilde Ferreira, Fernando Brederode, João de Matos Rodrigues, Joaquim José Martins, José de Almeida Belo, José Augusto dos Santos Lucas, Luciano José de Oliveira Ribeiro, Luciano Pereira da Silva, Luís Augusto Ferreira Martins, Luís Cabral e Sousa Teixeira de Morais, Luís Feliciano Marrecas Ferreira, Luís Felipe Leite Pinto, Luís da Silva Viegas, Octávio da Fonseca Brito and Pedro Teotónio Pereira: (Associação dos Actuários Portugueses, 1926). 138 Nevertheless, there is no documental archive of APA in possession of IPA. The founding members of the IPA (in a total of 78) are listed at (Caeiro and Barroso, 2005, 17–18). 139 (Queiroz de Barros, 1936). 140 Sociedade Portuguesa de Matemática, 1947. Regulamento interno da Sociedade Portuguesa de Matemática. Boletim da Sociedade Portuguesa de Matemática série B, vol. 1, n.o 1 (available at https://memoria.spm.pt/publicacoes). There were 10 Permanent Committees. The scientific ones were: Comissão Pedagógica (Pedagogical Committee) (5 members), Comissão de Matemática Pura (Pure Mathematics Committee) (3 members), Comissão de Matemática Aplicada (Applied Mathematics Committee) (5 members and between them specialists in mechanics, astronomy, statistics and actuarial calculus), Comissão de História e Filosofia da Matemática (History and Philosophy of Mathematics Committee) (3 members) and Comissão de História da Astronomia Náutica (Nautical History Committee) (3 members). 141 On the foundation of PMS see (Saraiva, 2012). On the history of PMS see (Morgado, 1995). 142 A list of the 331 members of PSM as on 1947 is available at https://memoria.spm.pt/socios_listagem.

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Meeting Organized by the Portuguese Mathematical Society (Óbidos, 16–18 November 2000). Acta Universitatis Conimbrigensis, Coimbra, pp. 601–627. Rosendo, V., 1990. Montepio Geral. 150 anos de história 1840–1990. Imprensa Nacional da Casa da Moeda, Lisboa. n.p. Rosendo, V., 1996. O mutualismo em Portugal: dois séculos de história e suas origens. Montepio Geral, Lisboa. n.p. Saint-Cyran, P.E.C.d., 1779. Calcul des rentes viagères sur une et sur plusieurs têtes. Chez Cellot & Jombert, Fils jeune, Libraires, Paris. Saint-Cyran, P.E.C.d., 1797. Calculo das pensões vitalicias por Saint-Cyran. Regia Typographica, Lisboa (translation by José Maria Dantas Pereira; ed. orig.: Saint-Cyran, P.E.C., 1779. Calcul des rentes viagères sur une et sur plusieurs têtes. Chez Cellot & Jombert, Paris). Santos, M.C.G.d., 1951. Ensaio duma tábua de morbidez portuguesa. Boletim [do Instituto dos Actuários Portugueses] 6, 147–149. Saraiva, A.P., 2011. Associativismo mutualista em Lisboa na segunda metade do século XIX (unpublished master’s thesis on contemporary and modern history). ISCTE - Instituto Universitário de Lisboa, Lisboa, Portugal. Saraiva, L., Pinto, J. (Eds.), 2010. Aureliano de Mira Fernandes (1884–1958). In: Proceedings of the Colloquium to Commemorate the 50th Anniversary of His Passing. Boletim da Sociedade Portuguesa de Matemática (número especial). 245 pp. Saraiva, L.M.R., 1993. On the first history of Portuguese mathematics. Historia Mathematica 20, 415–427. Saraiva, L.M.R., 1997. Historiography of mathematics in the works of Rodolfo Guimarães. Historia Mathematica 24, 86–97. Saraiva, L.M.R., 2004. Historiography of mathematics in Portugal. In: Saraiva, L., Leitão, H. (Eds.), The Practice of Mathematics in Portugal. Papers from the International Meeting Organized by the Portuguese Mathematical Society. Óbidos, 16–18 November 2000. Acta Universitatis Conimbrigensis, Coimbra, pp. 35–61. Saraiva, L.M.R., 2005. O início da actividade científica de Francisco Gomes Teixeira (1851–1933). In: Saraiva, L., Leitão, H. (Eds.), Proceedings of the 4th Luso-Brazilian Meeting on History of Mathematics. Natal, 24–27 October 2004. EDUFRN, Natal, pp. 161–176. Saraiva, L.M.R., 2008. Mathematics in the Memoirs of the Lisbon Academy of Sciences in the 19th century. Historia Mathematica 35, 302–326. Saraiva, L.M.R., 2012. A década prodigiosa da matemática portuguesa: os começos da Sociedade Portuguesa de Matemática (1936–1945). Revista Brasileira de História da Matemática 11 (23), 73–98. Sibbett, T., 2004. History of insurance. In: Teugels, J.L., Sundt, B. (Eds.), Encyclopedia of Actuarial Science, vol. II. John Wiley & Sons, New Jersey, pp. 842–862. Sousa, F.d., 1995. História da estatística em Portugal. Instituto Nacional de Estatística, Lisboa. Sousa, F.d., Alves, J.F., 1995. Aliança UAP: uma história de seguros. Aliança UAP, Lisboa. Sousa, F.d., Marques, A.H.d.O.c., 2004. Nova história de Portugal. Volume X: Portugal e a Regeneração. Editorial Presença, Lisboa. Teixeira, F.G., 1902. Apontamentos biographicos sobre Daniel Augusto da Silva. In: Obras sobre Mathematica do Dr. F. Gomes Teixeira, 1904–1915, vol. I. Imprensa da Universidade, Coimbra, pp. 259–272. União de Norwich, 1835. Companhia de seguros de vidas, penções vitalicias, sobrevivencias e dotações para crianças. Typographia de Filippe Nery, Lisboa. Veiga Beirão, F.A., 1888. Codigo commercial portuguez. Livraria Gutenberg, Lisboa. Walford, C., 1871–1880. The Insurance Cyclopædia. Charles and Edwin Layton, London. Ana Patrícia Martins graduated in Mathematics, by the University of Coimbra in 2001 and finished her PhD degree in the history and philosophy of sciences in 2013 by the University of Lisbon. She is an Associate Professor of the Polytechnic Institute of Viseu. She is a member of the Centro Interuniversitário de História das Ciências e da Tecnologia (CIUHCT) since 2007 and a member of the Advisory Board of the Seminário Nacional de História da Matemática (Portuguese National Seminar for the History of Mathematics) since 2013. Her research interests include history of mathematics (18th and 19th c.) and history of actuarial science.