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Ruin probabilities and overshoots for general Levy insurance risk processes


Reference:

Klppelberg, C., Kyprianou, A. E. and Maller, R. A., 2004. Ruin probabilities and overshoots for general Levy insurance risk processes. Annals of Applied Probability, 14 (4), pp. 1766-1801.

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Official URL:

http://dx.doi.org/10.1214/105051604000000927

Abstract

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.

Details

Item Type Articles
CreatorsKlppelberg, C., Kyprianou, A. E. and Maller, R. A.
DOI10.1214/105051604000000927
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code7228

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