Ruin probabilities for a regenerative Poisson gap generated risk process

Søren Asmussen () and Romain Biard ()
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Søren Asmussen: Department of Mathematical Sciences - Aarhus University [Aarhus]
Romain Biard: Department of Mathematical Sciences - Aarhus University [Aarhus]

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Abstract: 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.

Keywords: Ruin theory; Subexponential distribution; Large deviations; Markov additive process; Finite horizon ruin (search for similar items in EconPapers)
Date: 2011
New Economics Papers: this item is included in nep-rmg
Note: View the original document on HAL open archive server: https://hal.science/hal-00569254v2
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Published in European Actuarial Journal, 2011, 1 (1), pp.3-22. ⟨10.1007/s13385-011-0002-8⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00569254

DOI: 10.1007/s13385-011-0002-8

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