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2011
- handle: 10670/1.0df2fq
- hal: hal-00569254
- doi: 10.1007/s13385-011-0002-8
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Mots-clés
Ruin theory Subexponential distribution Large deviations Markov additive process Finite horizon ruinSujets proches
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Søren Asmussen et al., « Ruin probabilities for a regenerative Poisson gap generated risk process », HAL-SHS : économie et finance, ID : 10.1007/s13385-011-0002-8
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Résumé
A risk process with constant premium rate $c$ and Poisson arrivals of claims is considered. A threshold $r$ is defined for claim interarrival times, such that if $k$ consecutive interarrival times are larger than $r$, then the next claim has distribution $G$. Otherwise, the claim size distribution is $F$. Asymptotic expressions for the infinite horizon ruin probabilities are given for both light- and the heavy-tailed cases. A basic observation is that the process regenerates at each $G$-claim. Also an approach via Markov additive processes is outlined, and heuristics are given for the distribution of the time to ruin.