by Søren Asmussen (Aarhus University, Denmark) & Hansjörg Albrecher (University of Lausanne, Switzerland)

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.

• 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
• Stochastic Control
• Gerber–Shiu Functions
• Recent Developments in Monte Carlo Methods
• Recent Developments in Fluctuation Theory for Levy Processes
• Payment of Dividends
• Tail Estimation
• Dependent Risks
• Level-Dependent Risk Processes