Ruin Probabilities

Offers a comprehensive treatment of the classical and modern ruin probability theory. This title includes topics such as: Lundberg's inequality, the Cramer-Lundberg approximation, exact solutions, other approximations, finite horizon ruin probabilities, and extensions of the classical compound Poisson model to allow for reserve-dependent premiums.

The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber–Shiu functions and dependence.

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