Ruin Probabilities Synopsis
The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramer-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.
Ruin Probabilities Press Reviews
This book stands out as it incorporates the current science and research of the last few years as well as presents the link between queuing theory and other areas of applied probability theory. This book exceeds the merits of a standard textbook and it furthermore has the character of an encyclopedia with an impressive compilation of references (923 in total) and comments at the end of each section. It will surely become a standard reference work in the realm of ruin theory in the future. -- Jahresbericht der DMV Jahresbericht der DMV The book presents a valuable compendium, particularly in the area of current developments in the insurance industry, in order to respond to those developments with adequate risk control measures. The book is suitable for research purposes, teaching, self-learning as well as for practical application in insurance businesses. -- International Mathematical News International Mathematical News 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 Zentralblatt Maths 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 Short Book Reviews 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 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 in 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 Journal of the American Statistical Association