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• W3105156169 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." @default.
• W3105156169 created "2020-11-23" @default.
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• W3105156169 date "2004-11-01" @default.
• W3105156169 modified "2023-10-16" @default.
• W3105156169 title "Ruin probabilities and overshoots for general Lévy insurance risk processes" @default.
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• W3105156169 doi "https://doi.org/10.1214/105051604000000927" @default.
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