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.

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. For instance the blog of the famous statistician Andrew Gelman reacts to an article in the NY Times. 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.