Ruin Probabilities and Overshoots for General Levy Insurance Risk Processes

Details Ruin Probabilities and Overshoots for General Levy Insurance Risk Processes Ruin Probabilities and Overshoots for General Levy Insurance Risk Processes

2005-03-24

arxiv.org/abs/math/0503539v1

Annals of Applied Probability 2004, Vol. 14, No. 4, 1766-1801

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000927 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000927

We formulate the insurance risk process in a general Levy 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 -\infty a.s. and the positive tail of the Levy measure, or of the ladder height measure, is subexponential or, more generally, convolution equivalent. Results of Asmussen and Kluppelberg [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 Levy processes.

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