Modern Actuarial Risk Theory -- Using R

Rob Kaas
  University of Amsterdam, The Netherlands
Marc Goovaerts
  Catholic University of Leuven, Belgium
Jan Dhaene
  Catholic University of Leuven, Belgium
Michel Denuit
  Catholic University of Louvain-la-Neuve, Belgium

Contents: Foreword. Preface. 1. Utility theory and insurance. 2. The individual risk model. 3. Collective risk models. 4. Ruin theory. 5. Premium principles. 6. Bonus-malus systems. 7. Ordering of risks. 8. Credibility theory. 9. Generalized linear models. 10. IBNR techniques. 11. More on GLMs. Appendices: The 'R' in Modern ART, Hints for the exercises, Notes and references, Tables, Index.

Book cover Modern A.R.T. - Using R
Modern Actuarial Risk Theory -- Using R contains what every actuary needs to know about non-life insurance mathematics. It starts with the standard material like utility theory, individual and collective model and basic ruin theory. Other topics are risk measures and premium principles, bonus-malus systems, ordering of risks and credibility theory. It also contains some chapters about Generalized Linear Models, applied to rating and IBNR problems. As to the level of the mathematics, the book would fit in a bachelors or masters program in quantitative economics or mathematical statistics.
This second and much expanded edition emphasizes the implementation of these techniques through the use of R. This free but incredibly powerful software is rapidly developing into the de facto standard for statistical computation, not just in academic circles but also in practice. With R, one can do simulations, find maximum likelihood estimators, compute distributions by inverting transforms, and much more.

R is a free software environment for statistical computing and graphics. It compiles and runs on a wide variety of UNIX platforms, Windows and MacOS. To download R (about 36 Mb), go to its homepage.
Much material on R is to be found on the internet, and each year several new books about its application appear.

Changes in the second edition The main changes in the second edition are that there is now even more emphasis on actual practical use of risk theory. For example there is much more attention for parameter estimation in loss models. Risk measures such as TVaR are studied and compared for ordered pairs of risks. Comonotonicity is applied to get stochastic bounds on the cdf of a sum of lognormal random variables. Two case studies were added to the GLM chapter. Some simple IBNR-methods such as Chain Ladder and Bornhuetter-Ferguson are studied in more detail. The theoretical past of GLMs is extended, for example with Tweedie's compound Poisson-gamma model. To illustrate the use of R, some exploratory data analysis is done on a risk portfolio, and an artificial portfolio such as might be encountered in real life is generated.
The first edition contained 306 pages, the second has 381, with about 10% more contents on each page.

In October 2009, a soft-cover student version of the second edition appeared. In this version, all errors found in the hard-cover version of 2008 were eliminated.

e-book The book has its own homepage at Springer, where you can find out how to obtain it as an e-book.

Versions in other languages After forerunners in Dutch (1993, 1998), the first English edition of Modern Actuarial Risk Theory appeared in 2001. It has been translated into Chinese and Russian; the second edition (2008) is currently being translated into Chinese as well as Turkish.

Internet pages associated with the use of this book:

Support for teachers A solution manual containing solutions to virtually all the exercises in the book is available from the authors. Also, my own slides for classroom use are available for teachers. Both are more than 500 pages of pdf-files, suitable for projection using a beamer.
To get these files, contact us, adding some details like a homepage of yourself or of your institute, and about the course for which you intend to use these slides.

Feedback The authors very much appreciate getting feedback about the book. Is anything unclear, forgotten, just plain wrong, or clumsily done? Please let us know, as there might be updated versions of the book. If you have good things to say, you are welcome as well.

Page maintained by Rob Kaas.
Latest update of this page: November 2013