Description
Book SynopsisThe book is a comprehensive treatment of classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (eg. 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 or periodicity. Special features of the book are the emphasis on change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas like queueing theory.
Trade Review"This book is a must for anybody working in applied probability. It is a comprehensive treatment of the known results on ruin probabilities?" Short Book Reviews "This is an excellent handbook on the risk theory and brilliant encyclopedia in ruin probabilities results. This book will be useful both for graduate students who deal with stochastic models in insurance mathematics, experts in risk processes and also for those specialists who apply the methods of risk theory in practice." Zentralblatt Maths., 2001
Table of ContentsSome general tools and results; the compound Poisson model; premiums depending on the current reserve; the probability of ruin within finite time; renewal arrivals; risk theory in a Markovian environment; risk theory in a periodic environment; simulation methodology; miscellaneous topics. Appendices: phase-type distributions; selected background material.
