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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.
