Ruin Probabilities and Overshoots for GeneralLvy Insurance Risk Processes

We formulate the insurance risk process in a general Lvy 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 Lvy measure, or of the ladder height measure, is subexponential or, more generally, convolution equivalent. Results of Asmussen and Klppelberg [Stochastic Process. Appl. 64 (1996) 103125] and Bertoin and Doney [Adv. in Appl. Probab. 28 (1996) 207226] 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 Lvy processes.

Source
Institute of Mathematical Statistics
Length of Resource
36
Author
Claudia Klppelberg, Andreas E. Kyprianou and Ross A. Maller
Date Published
Publication Type
paper
Resource Type
academic

ResourceID: 72440

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