Risk modelling in general insurance. From principles to practice. (Q2898743)

From the cover: ``Knowledge of risk models and the assessment of risk is a fundamental part of the training of actuaries and all who are involved in financial, pensions and insurance mathematics. This book provides students and others with a firm foundation in a wide range of statistical and probabilistic methods for the modelling of risk, including short term risk modelling, model based pricing, risk sharing, ruin theory and credibility.''NEWLINENEWLINEAfter a short introduction, models for claim numbers and claim sizes are given, and (one-period) models for short term risks are introduced. For the collective models, in particular numerical methods (like Panjer's recursion and the fast Fourier transform) and approximations are discussed. A next chapter gives the usual premium calculation principles and introduces credibility methods for the pricing of collective contracts. Chapter five deals with several aspects of reinsurance. In particular, optimal reinsurance contracts are discussed from the point of view of a cedent or a reinsurer. Interesting is in particular the minimisation of the sum of variances for the cedent and the reinsurer, which gives in some sense an optimal contract for both players. Chapter six gives an introduction to classical ruin theory. A final chapter deals with case studies; in particular useful for the reader to see the applications of the theory presented in the book. In an appendix, an introduction to utility theory and the solutions to all the exercises are given.NEWLINENEWLINEThis book is written for actuaries preparing for the actuarial exams and for students. The prerequisites are just a basic knowledge of mathematics, probability and statistics on the level that students learn in social sciences; so the book is understandable for a broad audience. The theory is well explained. Each chapter and section starts with an overview of the topic. Many examples help to understand, motivate the theory and give a good feeling for the applications. I like very much the illustrations with programs in \texttt{R}. The book also discusses statistical aspects, which is, even though an important issue, often missing in text books on actuarial science. What I am missing are the Poisson limit theorems in the individual model and the useful formulae \(E[\min\{X,M\}] = \int_0^M (1-F_X(t))\;d t\) and \(E[\max\{X-M,0\}] = \int_M^\infty (1-F_X(t))\;d t\), which I think each actuary should know.NEWLINENEWLINEVery nice are the considerations on optimal reinsurance. A large variety of optimisation problems are discussed, giving the reader a good feeling how reinsurance contracts reduce the risk. Very helpful are the case studies, where the reader gets acquainted with the effect of the parameters in the premium calculation principles, and of reinsurance on the expected payments and on the ruin probability. These effects are illustrated with graphs. The exercises ending the chapters help the reader to build the intuition behind the theory and to apply the topics treated in the book. All in all, I can recommend the book; in particular, for the audience for whom it is written.