RUIN PROBABILITIES by Søren Asmussen (Lund University, Sweden) The 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.

Contents:

Introduction Some General Tools and Results The Compound Poisson Model The Probability of Ruin within Finite Time Renewal Arrivals Risk Theory in a Markovian Environment Premiums Depending on the Current Reserve Matrix–Analytic Methods Ruin Probabilities in the Presence of Heavy Tails Simulation Methodology Miscellaneous Topics

Readership: Applied mathematicians.

“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

“This is a very valuable research monograph, dealing with an area that is mathematically attractive and of considerable relevance to insurance applications. I recommend the book to both experts and beginners in the field.”

Mathematical Reviews

“No other book covers such a vast area, at least none that is so up-to-date … one can see that Ruin Probabilities is invaluable for researchers in risk theory and perhaps other fields in applied probability. The book can also be used as a textbook for a graduate-level course on ruin theory … The teacher's task is made easy by the recommendation on the introduction on how to get started with the book, and then how to proceed in a second reading.”

Journal of the American Statistical Association

400pp    Pub. date: Jul 2000