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Practical risk theory for actuaries.
Abstracts and Reviews
063009 (MOl) Markov models and optimization. Davis M.H.A., Monographs on Statistics Probability,
Chapman
and Applied
and Hall, 1993, 295 pp.
Stochastic control theory has for many years attracted the interest of actuarial researchers, since there are many practical insurance problems that can be expressed by means of this theory. Continuous-time stochastic control theory has until now achieved most of its results in the domain of systems driven by stochastic differential equations. This is due to the close connection with the theory of partial differential equations and to the fact that that theory is so well-developed. The limitations of the theory are that the systems that can be studied in many cases are too far from the real situations. This book presents a new direction which studies piecewise-deterministic Markov processes, so-called PDP models. These models can be made much more realistic, although they pose new problems as regards finding solutions. The models are connected with systems of integro-differentktt equations for which there is no unified theory such as exists for partial differential equations. Such integro-differential equations can, however, be solved by a simple recursive method that allows efficient computation. The table of contents of the book is as follows: 1. Analysis, probability and stochastic processes 2. Piecewise-deterministic Markov processes 3. Distributions and expectations 4. Control theory 5. Control by intervention Appendix: Jump processes and their martingales. (B. Palmgren) Keywords:
Stochastic
Processes,
Markov
Processes,
PDP models.
73
practically-oriented minds. The book is divided in two parts. Part I, Foundations of Practical Risk Theory, covers the standard basic themes: the number of claims and claim amount random variables, the calculation of the distribution of the aggregate claims, etc. It also discusses the use and implementation of the simulation techniques (or Monte-Carlo methods) to obtain the desired quantities (ruin probabilities, expectations, etc.). The models presented in Part II are generally so complex that there is no hope to develop analytical results, and for these reasons the authors rely heavily on simulation. Part II, Stochastic Analysis of Insurance Business, deals with “the analysis of variability of assets and liabilities with a short- and long-term horizon and practical aspects of modelling the insurance business”. The authors address the problem of taking into account inflation, investment returns, expenses, taxes and dividends. The last two chapters are devoted to life insurance and pension “schemes” (pension funds, trusts, etc.) from both the deterministic and stochastic point of view. Part I is intended to be used as a primary text-book and contains a number of exercises while they are quite rare in Part II. This latter part is dedicated to the practicing actuary who will find it a plentiful source of inspiration when building his own models. This text is easy to read since the level of mathematical sophistication is kept low, emphasis being given to the practical aspects of (F. Dufresne) applying risk theory. Keywords:
Risk Theory, Insurance
Business.
063011 (MOl)
Unbiased loss development factors. Murphy D.M., Casualty Actuarial Society Forum,
Vol.
I, 1994, pp. 183-246. 063010 (MOl)
Practical risk theory for actuaries. Daykin C.D., Pentiklinen T., Pesonen M., Mtteilungen der Vereinigung schweizerischer Versicherungsmathematiker, Heft I, 1994, pp. 98. Over the years, the book Risk Theory: The stochastic basis of insurance has evolved from a concise monograph to a voluminous book now entitled Practical risk theory for actuaries that is meant as a replacement to
the older book. The successor of the late R.E. Beard is C.D. Daykin who joined his effort to those of the other authors to write - in fact - a new book more up to date and for the
Casualty Actuarial Society literature is inconclusive regarding whether the loss development technique is biased or unbiased, or which of the traditional methods of estimating link ratios is best. This paper presents a mathematical framework to answer those questions for the class of linear link ratio estimators used in practice. A more accurate method of calculating link ratios is derived based on classical regression theory. The circumstances under which the traditional methods could be considered optimal are discussed. It is shown that two traditional estimators may in fact be least squares estimators depending on the set of assumptions one believes governs the process of loss development. Formulas for variances of, and confidence intervals
063009 (MOl) Markov models and optimization. Davis M.H.A., Monographs on Statistics Probability,
Chapman
and Applied
and Hall, 1993, 295 pp.
Stochastic control theory has for many years attracted the interest of actuarial researchers, since there are many practical insurance problems that can be expressed by means of this theory. Continuous-time stochastic control theory has until now achieved most of its results in the domain of systems driven by stochastic differential equations. This is due to the close connection with the theory of partial differential equations and to the fact that that theory is so well-developed. The limitations of the theory are that the systems that can be studied in many cases are too far from the real situations. This book presents a new direction which studies piecewise-deterministic Markov processes, so-called PDP models. These models can be made much more realistic, although they pose new problems as regards finding solutions. The models are connected with systems of integro-differentktt equations for which there is no unified theory such as exists for partial differential equations. Such integro-differential equations can, however, be solved by a simple recursive method that allows efficient computation. The table of contents of the book is as follows: 1. Analysis, probability and stochastic processes 2. Piecewise-deterministic Markov processes 3. Distributions and expectations 4. Control theory 5. Control by intervention Appendix: Jump processes and their martingales. (B. Palmgren) Keywords:
Stochastic
Processes,
Markov
Processes,
PDP models.
73
practically-oriented minds. The book is divided in two parts. Part I, Foundations of Practical Risk Theory, covers the standard basic themes: the number of claims and claim amount random variables, the calculation of the distribution of the aggregate claims, etc. It also discusses the use and implementation of the simulation techniques (or Monte-Carlo methods) to obtain the desired quantities (ruin probabilities, expectations, etc.). The models presented in Part II are generally so complex that there is no hope to develop analytical results, and for these reasons the authors rely heavily on simulation. Part II, Stochastic Analysis of Insurance Business, deals with “the analysis of variability of assets and liabilities with a short- and long-term horizon and practical aspects of modelling the insurance business”. The authors address the problem of taking into account inflation, investment returns, expenses, taxes and dividends. The last two chapters are devoted to life insurance and pension “schemes” (pension funds, trusts, etc.) from both the deterministic and stochastic point of view. Part I is intended to be used as a primary text-book and contains a number of exercises while they are quite rare in Part II. This latter part is dedicated to the practicing actuary who will find it a plentiful source of inspiration when building his own models. This text is easy to read since the level of mathematical sophistication is kept low, emphasis being given to the practical aspects of (F. Dufresne) applying risk theory. Keywords:
Risk Theory, Insurance
Business.
063011 (MOl)
Unbiased loss development factors. Murphy D.M., Casualty Actuarial Society Forum,
Vol.
I, 1994, pp. 183-246. 063010 (MOl)
Practical risk theory for actuaries. Daykin C.D., Pentiklinen T., Pesonen M., Mtteilungen der Vereinigung schweizerischer Versicherungsmathematiker, Heft I, 1994, pp. 98. Over the years, the book Risk Theory: The stochastic basis of insurance has evolved from a concise monograph to a voluminous book now entitled Practical risk theory for actuaries that is meant as a replacement to
the older book. The successor of the late R.E. Beard is C.D. Daykin who joined his effort to those of the other authors to write - in fact - a new book more up to date and for the
Casualty Actuarial Society literature is inconclusive regarding whether the loss development technique is biased or unbiased, or which of the traditional methods of estimating link ratios is best. This paper presents a mathematical framework to answer those questions for the class of linear link ratio estimators used in practice. A more accurate method of calculating link ratios is derived based on classical regression theory. The circumstances under which the traditional methods could be considered optimal are discussed. It is shown that two traditional estimators may in fact be least squares estimators depending on the set of assumptions one believes governs the process of loss development. Formulas for variances of, and confidence intervals