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

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.
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Romain Biard, Claude Lefèvre, Stéphane Loisel, Haikady Nagaraja. Asymptotic Finite-Time Ruin Probabilities for a Class of Path-Dependent Heavy-Tailed Claim Amounts Using Poisson Spacings. Applied Stochastic Models in Business and Industry, Wiley, 2011, 27 (5), pp.503-518. ⟨10.1002/asmb.857⟩. ⟨hal-00409418⟩

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