Ruin probabilities and overshoots for general Lévy insurance risk processes
Top Cited Papers
Open Access
- 1 November 2004
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 14 (4), 1766-1801
- https://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.Keywords
This publication has 33 references indexed in Scilit:
- Ruin probabilities and decompositions for general perturbed risk processesThe Annals of Applied Probability, 2004
- Convolution equivalence and infinite divisibilityJournal of Applied Probability, 2004
- VOTRE LÉVY RAMPE-T-IL?Journal of the London Mathematical Society, 2002
- The supremum of a negative drift random walk with dependent heavy-tailed stepsThe Annals of Applied Probability, 2000
- Some asymptotic results for transient random walksAdvances in Applied Probability, 1996
- Convolutions of Distributions With Exponential and Subexponential TailsJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1987
- A property of the generalized inverse Gaussian distribution with some applicationsJournal of Applied Probability, 1983
- Degeneracy Properties of Subcritical Branching ProcessesThe Annals of Probability, 1973
- The strong law of large numbers when the mean is undefinedTransactions of the American Mathematical Society, 1973
- Renewal Theorems When the First or the Second Moment is InfiniteThe Annals of Mathematical Statistics, 1968