Here is a modern review of the problem of ruin for the classical Cramér-Lundberg model and the surplus of an insurance company. Covers martingales and path decompositions for analysing distribution of the time of ruin, wealth prior to ruin and deficit at ruin.

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 CramérLundberg 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 explored.

Gerber-Shiu Risk Theory can be used as lecture notes and is suitable for a graduate course. Each chapter corresponds to approximately two hours of lectures.

Provides a self-contained and easy-to-read introduction to classical ruin theory Includes recent developments in exotic ruin theory Makes transparent the connection with the theory of spectrally negative Lévy processes Includes supplementary material: sn.pub/extras

Autorentext

Andreas Kyprianou has a degree in Mathematics from the University of Oxford and a Ph.D. in Probability Theory from The University of Sheffield. He is currently a Professor of Probability at the University of Bath, having held academic positions in Mathematics and Statistics Departments at the London School of Economics, Edinburgh University, Utrecht University and Heriot-Watt University, besides working for nearly two years as a research mathematician in the oil industry. His research is focused on pure and applied probability.

Inhalt
Introduction.- The Wald martingale and the maximum.- The Kella-Whitt martingale and the minimum.- Scale functions and ruin probabilities.- The GerberShiu measure.- Reflection strategies.- Perturbation-at-maximum strategies.- Refraction strategies.- Concluding discussion.- References.