Asymptotic Finite-Time Ruin Probabilities for a Class of Path-Dependent Heavy-Tailed Claim Amounts Using Poisson Spacings

Romain Biard (romain.biard@univ-fcomte.fr), Claude Lefèvre (clefevre@ulb.ac.be), Stéphane Loisel and Haikady Nagaraja (hnn@stat.osu.edu)
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Romain Biard: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Claude Lefèvre: ULB - Département de Mathématique [Bruxelles] - ULB - Faculté des Sciences [Bruxelles] - ULB - Université libre de Bruxelles
Haikady Nagaraja: Department of Statistics - OSU - The Ohio State University [Columbus]

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Abstract: In the compound Poisson risk model, several strong hypotheses may be found too restrictive to describe accurately the evolution of the reserves of an insurance company. This is especially true for a company that faces natural disaster risks like earthquake or flooding. For such risks, claim amounts are often inter-dependent and they may also depend on the history of the natural phenomenon. The present paper is concerned with a situation of this kind where each claim amount depends on the previous interclaim arrival time, or on past interclaim arrival times in a more complex way. Our main purpose is to evaluate, for large initial reserves, the asymptotic finite-time ruin probabilities of the company when the claim sizes have a heavy-tailed distribution. The approach is based more particularly on the analysis of spacings in a conditioned Poisson process.

Keywords: Risk process; path-dependent claims; heavy-tailed claim amounts; Poisson spacing; finite-time ruin probabilities; asymptotic approximation for large initial reserves (search for similar items in EconPapers)
Date: 2011
Note: View the original document on HAL open archive server: https://hal.science/hal-00409418v1
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Published in Applied Stochastic Models in Business and Industry, 2011, 27 (5), pp.503-518. ⟨10.1002/asmb.857⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00409418

DOI: 10.1002/asmb.857

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