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 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.
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