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Motivated by the many and long-standing contributions of H. Gerber and E. Shiu, this book gives a modern perspective on the problem of ruin for the classical Cramer-Lundberg model and the surplus of an insurance company. The book studies martingales and path decompositions, which are the main tools used in analysing the distribution of the time of ruin, the wealth prior to ruin and the deficit at ruin. Recent developments in exotic ruin theory are also considered. In particular, by making dividend or tax payments out of the surplus process, the effect on ruin is...

Levy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes.

This textbook is based on a series of graduate courses concerning the theory and application of Levy processes from the...

This is the second volume in a subseries of the Lecture Notes in Mathematics called Levy Matters, whichis published at irregular intervals over the years. Each volume examines a number of key topics in the theory or applications of Levy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world.
The expository articles in this second volume cover two important topics in the area of Levy processes.
The first article by Serge Cohen reviews the most
important findings on fractional Levy fields to date in a...