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

Romain Biard (1) , Claude Lefèvre (2) , Stéphane Loisel (1) , Haikady Nagaraja (3)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 ULB - Département de Mathématique [Bruxelles]
3 Department of Statistics

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

Domains: Economics and Finance; Probability [math.PR]; Combinatorics [math.CO]

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, 2011, 27 (5), pp.503-518. ⟨10.1002/asmb.857⟩. ⟨hal-00409418⟩