Ruin probabilities and overshoots for general Levy insurance risk processes

Claudia Klppelberg, Andreas E Kyprianou, Ross A Maller

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123 Citations (SciVal)


We formulate the insurance risk process in a general Lévy process setting, and give general theorems for the ruin probability and the asymptotic distribution of the overshoot of the process above a high level, when the process drifts to −∞ a.s. and the positive tail of the Lévy measure, or of the ladder height measure, is subexponential or, more generally, convolution equivalent. Results of Asmussen and Klüppelberg [Stochastic Process. Appl. 64 (1996) 103–125] and Bertoin and Doney [Adv. in Appl. Probab. 28 (1996) 207–226] for ruin probabilities and the overshoot in random walk and compound Poisson models are shown to have analogues in the general setup. The identities we derive open the way to further investigation of general renewal-type properties of Lévy processes.
Original languageEnglish
Pages (from-to)1766-1801
Number of pages36
JournalAnnals of Applied Probability
Issue number4
Publication statusPublished - 2004


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