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Asymptotic finite-time ruin probabilities for a class of path-dependent heavy-tailed claim amount using Poisson spacings

par Biard, R.;Lefèvre, Claude ;Loisel, Sébastien ;Nagaraja, H.N.
Référence Applied stochastic models in business and industry, 27, page (503-518)
Publication Publié, 2011

Article révisé par les pairs

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Résumé :

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 claim inter-arrival time, or on past claim inter-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. © 2010 John Wiley & Sons, Ltd.