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Modern actuarial risk theory. Using R. 2nd ed. (English) Zbl 1148.91027
Berlin: Springer (ISBN 978-3-540-70992-3/hbk). xviii, 381 p. (2008).
The book gives a comprehensive survey of non-life insurance mathematics. Apart from the standard theory, it contains methods directly relevant for actuarial practice, for example the rating of automobile insurance policies, premium principles and risk measures, and IBNR models. In the second edition of the book, the theory is even more directly applicable by using the software R. It is an open source object oriented implementation of the language S with accent on statistical routines.
The book consists of 11 chapters as follows:
1. The expected utility model
2. The individual risk model
3. Collective risk models
4. The ruin model
5. Premium principles and risk measures
6. Bonus-malus system
7. Ordering of risks
8. Credibility theory
9. Generalized linear models
10. IBNR techniques
11. More on GLMs
The topics in the first five chapters are basic for non-life actuarial science. The remaining chapters contain short introductions to other topics traditionally regarded as non-life actuarial science.
Originally written for use with the actuarial science programs at the Universities of Amsterdam and Leuven, it is now in use at many other universities as well as for the non-academic actuarial education program organized by the Dutch Actuarial Society.
The methods presented can not only be used in non-life insurance, but also in other branches of actuarial science, as well as in actuarial practice.

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
62-02 Research exposition (monographs, survey articles) pertaining to statistics
91-02 Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance