Stochastic models in actuarial risk theory. A mathematical introduction (Q5920339)

In order to analyse a risky position in non-life insurance, the theory of stochastic models plays an important role. In this book, the most convenient tools for such an analysis are introduced. Starting from loss distributions, extreme value theory as well as coherent risk measures are discussed. Then, counting processes, in particular the Poisson process, are introduced, and the properties are applied to ruin theory. The results are then generalised by using renewal theory and exponential change of measure. In an appendix, the basic results from probability theory and analysis are given in order to give the reader all the basic tools to understand the actuarial theory. The book is mainly useful for practitioners. Many results are given without proof or with a mathematically non-rigorous but intuitive proof, so that the reader does not have to struggle with the mathematics but can get the intuition behind the actuarial methods. Links to other subjects like reliability or extreme value theory make a bridge to the mathematical theory, such that an interested reader sees where to look for further material. Unfortunately, some errors have made the way into the book. For example, Theorem 2.39 is wrong. The excess function diverges to infinity for all long-tailed distributions, which need not to be subexponential. However, the result would be correct for the usual distributions used in actuarial models.