Ruin probabilities and overshoots for general Levy insurance risk processes

Claudia Klppelberg, Andreas E Kyprianou, Ross A Maller

Research output: Contribution to journalArticle

106 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)1766-1801
Number of pages36
JournalAnnals of Applied Probability
Volume14
Issue number4
DOIs
Publication statusPublished - 2004

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Risk Process
Ruin Probability
Overshoot
Lévy Process
Insurance
Ladder Height
Lévy Measure
Compound Poisson
Poisson Model
Renewal
Asymptotic distribution
Stochastic Processes
Convolution
Tail
Random walk
Analogue
Theorem
Lévy process
Ruin probability
Insurance risk

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Ruin probabilities and overshoots for general Levy insurance risk processes. / Klppelberg, Claudia; Kyprianou, Andreas E; Maller, Ross A.

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

Research output: Contribution to journalArticle

Klppelberg, Claudia ; Kyprianou, Andreas E ; Maller, Ross A. / Ruin probabilities and overshoots for general Levy insurance risk processes. In: Annals of Applied Probability. 2004 ; Vol. 14, No. 4. pp. 1766-1801.
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