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An open group long-term care model.
Abstracts and Reviews MOO: GENERAL
AND MISCELLANEOUS
063001 (MOO, BlO) Unitised with profits - Gamaliel’s
advice.
Terra Nova Insurance, London, UK, Journal of the Institute of Actuaries, Vol. 120, Part III, 1993, pp. 415-469. The paper deals with the development of unitised with-profits business in the United Kingdom. The authors trace the recent history of these products and comment on the main reasons for their development. They also deal with corporate issues, including implications for policyholders and shareholders of different fund structures and different types of life office. Pricing and product development issues are also covered. Reserving issues including the range of valuation methods, statutory requirements and policyholders’ reasonable expectations are explored. Finally the paper considers the actuary’s contribution to the management of unitised with-profits policyholders’ expectations. (Authors) Keywords: Unitised With Profits, Product Design, Policyholders’ Reasonable Expectations, Valuation. O’Neill
J.E., Froggatt
H.W.,
063002 (MOO, BlO) Identities
for present values of life insurance
benefits.
R., Scandinavian Actuarial Journal, nr. 2, 1993, pp. 100-106. The rule of integration by parts produces useful formulas for the present value of a payment stream. Applied to life insurance, utilizing the counting process nature of the development of the policy, the rule induces three classes of identities, some generalizing certain classical relationships between life annuities and assurances and some not hitherto encountered in the litera(Author) ture. Insurance, Keywords: Life Payment Streams, Discounting, Counting Process. Norberg
71
able to absorb ever-increasing numbers and amounts of losses. They are already now exposed to the limits of their abilities. In property damage insurance, agreeing on adequate deductibles could help to concentrate the limited funds on the coverage of major losses. Third party liability insurers, who are far from having overcome the American asbestosis disaster, are threatened by an immense new potential of damage to the environment. If it is intended to back up the capacity of insurance markets by additional sources of coverage, for instance by governmental aids, these should be established in the form of reinsurance in conformity with existing market mechanisms. (Author) Keywords: Sources of Coverage, Reinsurance, Indemnity Insurance, Third Party Liability.
063004 (MOO, BlO) Sparen in der Lebensversicherung?
Terminologische Anmerkungen zu Leistung und Erfolg von Lebensversicherungsunternehmen(Saving in life insurance terminological notes regarding performance and success of life insurance companies). Schiiler W., Bielefield, Zeitschrifr fiir die gesamte Versicherungswissenschaft, Vol. 81. 1992, pp. 235-248. The paper discusses some production theoretical aspects of life insurance. It is emphasized that a life insurer maintains processes of risk protection by combining individual risks into a collective. This process differs essentially from the savings process offered by a bank - despite of the actuarial term of a savings premium and despite of (in some features) perhaps comparable results. As one of the consequences, the total premium is indeed - in contrast to the deposit in a savings institute - to be considered as the firm’s revenue. The paper also pleads for a clear distinction between positions of real expense and those of profit utilization which is not given in the present profit and loss accounting scheme for German insurers. (Author) Keywords: Saving, Life Insurance.
063003 (MOO, B41, B90) Deckungsmodelle und GroR-und Kumulrisiken
Regulierungskonzepte fir in der Schadenversicherung
(Coverage models and regulation concepts for major and cumulative risks in indemnity insurance). Schmidt G., Hannover, Zeitschrifr ftir die gesamte Versicherungswissenschaft, Vol. 81, 1992, pp. 191-203. The international insurance markets are no longer
MOZ: MODELLING
GENERAL
063005 (MOl) An open group long-term care model. Jones B.L., Willmit G.E., Scandinavian
Journal, nr. 2, 1993, pp. 161-I 72.
Actuarial
72
Abstracts and Revie ws
This paper presents a stochastic model for analyzing long-term care requirements and costs in a open group setting. Individuals are assumed to enter the elderly community according to a non-homogeneous Poisson process and move amongst the various levels of care according to an unspecified stochastic process. Distributions of the future population in each state are obtained. Assuming known cost functions, the distributions of the instantaneous annual cost of care and the present value of future costs are examined. The distribution of the present value of costs associated with entrants to the community during a given period is characterized by its Laplace transform. This transform is expressed in terms of the transform of the present value for a given individual. Under certain conditions the probability density function can be found. Asymptotic tail results are also considered. (Authors) Keywords: Long-Term Care, Non-HomogeneousPoisson Process, Present Value of Future Costs, Asymptotic Tail Probabilities.
063006 (MOl, BlO) One approach to dual randomness in life insurance. Beekman J.A., Fuelling C.P., Scandinavian Actuarial Journal, nr. 2, 1993, pp. 173-182. A model is presented which can be used when interest rates and future lifetimes are random, for life insurance. Expressions for the mean values and the standard deviations of a future life insurance payment are obtained. These can be used in determining contingency reserves and premium margins for possible adverse interest and mortality experience for a portfolio of life insurance policies. Four complete examples are considered, including four tables of values. (Authors) Keywords: Random Interest Rates, Joint Randomness in Interest and Mortality, Ornstein-Uhlenbeck Stochastic Process, Wiener Stochastic Process.
063007 (MOl) Hierarchical Bayesian Whittaker Graduation. Carlin B.P., Klugman S.A., Scandinavian Actuarial Journal, nr. 2, 1993, pp. 183-196. The Whittaker method of graduation has been known and used for a long time and has remained popular due to its possession of a number of ideal properties. They include being nonparametric and having an easy to understand foundation. The latter means that it makes sense and thus the user of the method has a good idea
of what it can and cannot do. As well, there is a statistical derivation available that uses Bayesian notions. A problem with the derivation is that it is more intuitive than precise and as such does not provide a useful frame of reference for the graduator. Regardless of the point of view, the graduation cannot be completed until the smoothing parameter is selected and this has always relied on the judgement of the analyst. In this paper, three tasks will be undertaken. The first is to replace the ad-hoc Bayesian derivation of the method with a formal Bayesian specification. The second is to show that with this specification it is possible to complete the graduation without making an arbitrary selection of the smoothing parameter. The third is to provide a Monte Carlo Bayesian approach for the incorporation of constraints in the graduated values. The ideas will be illustrated with a numerical example. (Authors) Keywords: Constrained Smoothing, Gibbs Samples, Life Tables, Prior Distribution.
063008 (MOl) Aspects of risk theory. Grandell J., Springer Series in Statistics, Probability and its Applications, Springer Verlag, 1992, I76 pp. This monograph on risk theory can be seen as representing over 90 years of research but making use of the modern tools of stochastic processes. The author has more than 20 years of experience in the field and is one of the links in an almost century-long Swedish research tradition. The book is not a textbook in risk theory, nor is it an exhaustive treatment of the vast subject. The table of contents is as follows: 1, The classical risk model 2. Generalizations of the classical risk model 3. Renewal models 4. Cox models 5. Stationary models Appendix. Finite time ruin probabilities. The emphasis is on risk models based on more general occurrence processes than the classical Poisson model. The presentation is theoretical in manner and scope, but the theory leads to practical implications, e.g. by deducing generalisations and indicating parallels which can be further be exploited by applying numerical methods or simulation. (B. Palmgren) Keywords: Risk theory Stochastic Processes, Cox Models, Renewal Models.
AND MISCELLANEOUS
063001 (MOO, BlO) Unitised with profits - Gamaliel’s
advice.
Terra Nova Insurance, London, UK, Journal of the Institute of Actuaries, Vol. 120, Part III, 1993, pp. 415-469. The paper deals with the development of unitised with-profits business in the United Kingdom. The authors trace the recent history of these products and comment on the main reasons for their development. They also deal with corporate issues, including implications for policyholders and shareholders of different fund structures and different types of life office. Pricing and product development issues are also covered. Reserving issues including the range of valuation methods, statutory requirements and policyholders’ reasonable expectations are explored. Finally the paper considers the actuary’s contribution to the management of unitised with-profits policyholders’ expectations. (Authors) Keywords: Unitised With Profits, Product Design, Policyholders’ Reasonable Expectations, Valuation. O’Neill
J.E., Froggatt
H.W.,
063002 (MOO, BlO) Identities
for present values of life insurance
benefits.
R., Scandinavian Actuarial Journal, nr. 2, 1993, pp. 100-106. The rule of integration by parts produces useful formulas for the present value of a payment stream. Applied to life insurance, utilizing the counting process nature of the development of the policy, the rule induces three classes of identities, some generalizing certain classical relationships between life annuities and assurances and some not hitherto encountered in the litera(Author) ture. Insurance, Keywords: Life Payment Streams, Discounting, Counting Process. Norberg
71
able to absorb ever-increasing numbers and amounts of losses. They are already now exposed to the limits of their abilities. In property damage insurance, agreeing on adequate deductibles could help to concentrate the limited funds on the coverage of major losses. Third party liability insurers, who are far from having overcome the American asbestosis disaster, are threatened by an immense new potential of damage to the environment. If it is intended to back up the capacity of insurance markets by additional sources of coverage, for instance by governmental aids, these should be established in the form of reinsurance in conformity with existing market mechanisms. (Author) Keywords: Sources of Coverage, Reinsurance, Indemnity Insurance, Third Party Liability.
063004 (MOO, BlO) Sparen in der Lebensversicherung?
Terminologische Anmerkungen zu Leistung und Erfolg von Lebensversicherungsunternehmen(Saving in life insurance terminological notes regarding performance and success of life insurance companies). Schiiler W., Bielefield, Zeitschrifr fiir die gesamte Versicherungswissenschaft, Vol. 81. 1992, pp. 235-248. The paper discusses some production theoretical aspects of life insurance. It is emphasized that a life insurer maintains processes of risk protection by combining individual risks into a collective. This process differs essentially from the savings process offered by a bank - despite of the actuarial term of a savings premium and despite of (in some features) perhaps comparable results. As one of the consequences, the total premium is indeed - in contrast to the deposit in a savings institute - to be considered as the firm’s revenue. The paper also pleads for a clear distinction between positions of real expense and those of profit utilization which is not given in the present profit and loss accounting scheme for German insurers. (Author) Keywords: Saving, Life Insurance.
063003 (MOO, B41, B90) Deckungsmodelle und GroR-und Kumulrisiken
Regulierungskonzepte fir in der Schadenversicherung
(Coverage models and regulation concepts for major and cumulative risks in indemnity insurance). Schmidt G., Hannover, Zeitschrifr ftir die gesamte Versicherungswissenschaft, Vol. 81, 1992, pp. 191-203. The international insurance markets are no longer
MOZ: MODELLING
GENERAL
063005 (MOl) An open group long-term care model. Jones B.L., Willmit G.E., Scandinavian
Journal, nr. 2, 1993, pp. 161-I 72.
Actuarial
72
Abstracts and Revie ws
This paper presents a stochastic model for analyzing long-term care requirements and costs in a open group setting. Individuals are assumed to enter the elderly community according to a non-homogeneous Poisson process and move amongst the various levels of care according to an unspecified stochastic process. Distributions of the future population in each state are obtained. Assuming known cost functions, the distributions of the instantaneous annual cost of care and the present value of future costs are examined. The distribution of the present value of costs associated with entrants to the community during a given period is characterized by its Laplace transform. This transform is expressed in terms of the transform of the present value for a given individual. Under certain conditions the probability density function can be found. Asymptotic tail results are also considered. (Authors) Keywords: Long-Term Care, Non-HomogeneousPoisson Process, Present Value of Future Costs, Asymptotic Tail Probabilities.
063006 (MOl, BlO) One approach to dual randomness in life insurance. Beekman J.A., Fuelling C.P., Scandinavian Actuarial Journal, nr. 2, 1993, pp. 173-182. A model is presented which can be used when interest rates and future lifetimes are random, for life insurance. Expressions for the mean values and the standard deviations of a future life insurance payment are obtained. These can be used in determining contingency reserves and premium margins for possible adverse interest and mortality experience for a portfolio of life insurance policies. Four complete examples are considered, including four tables of values. (Authors) Keywords: Random Interest Rates, Joint Randomness in Interest and Mortality, Ornstein-Uhlenbeck Stochastic Process, Wiener Stochastic Process.
063007 (MOl) Hierarchical Bayesian Whittaker Graduation. Carlin B.P., Klugman S.A., Scandinavian Actuarial Journal, nr. 2, 1993, pp. 183-196. The Whittaker method of graduation has been known and used for a long time and has remained popular due to its possession of a number of ideal properties. They include being nonparametric and having an easy to understand foundation. The latter means that it makes sense and thus the user of the method has a good idea
of what it can and cannot do. As well, there is a statistical derivation available that uses Bayesian notions. A problem with the derivation is that it is more intuitive than precise and as such does not provide a useful frame of reference for the graduator. Regardless of the point of view, the graduation cannot be completed until the smoothing parameter is selected and this has always relied on the judgement of the analyst. In this paper, three tasks will be undertaken. The first is to replace the ad-hoc Bayesian derivation of the method with a formal Bayesian specification. The second is to show that with this specification it is possible to complete the graduation without making an arbitrary selection of the smoothing parameter. The third is to provide a Monte Carlo Bayesian approach for the incorporation of constraints in the graduated values. The ideas will be illustrated with a numerical example. (Authors) Keywords: Constrained Smoothing, Gibbs Samples, Life Tables, Prior Distribution.
063008 (MOl) Aspects of risk theory. Grandell J., Springer Series in Statistics, Probability and its Applications, Springer Verlag, 1992, I76 pp. This monograph on risk theory can be seen as representing over 90 years of research but making use of the modern tools of stochastic processes. The author has more than 20 years of experience in the field and is one of the links in an almost century-long Swedish research tradition. The book is not a textbook in risk theory, nor is it an exhaustive treatment of the vast subject. The table of contents is as follows: 1, The classical risk model 2. Generalizations of the classical risk model 3. Renewal models 4. Cox models 5. Stationary models Appendix. Finite time ruin probabilities. The emphasis is on risk models based on more general occurrence processes than the classical Poisson model. The presentation is theoretical in manner and scope, but the theory leads to practical implications, e.g. by deducing generalisations and indicating parallels which can be further be exploited by applying numerical methods or simulation. (B. Palmgren) Keywords: Risk theory Stochastic Processes, Cox Models, Renewal Models.