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

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  • Romain Biard
  • Claude Lefèvre
  • Stéphane Loisel
  • Haikady N. Nagaraja

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 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. Copyright © 2010 John Wiley & Sons, Ltd.

Suggested Citation

  • Romain Biard & Claude Lefèvre & Stéphane Loisel & Haikady N. Nagaraja, 2011. "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, John Wiley & Sons, vol. 27(5), pages 503-518, September.
    • Handle: RePEc:wly:apsmbi:v:27:y:2011:i:5:p:503-518
    DOI: 10.1002/asmb.857
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    Cited by:

    1. Li, Xiaohu & Wu, Jintang, 2014. "Asymptotic tail behavior of Poisson shot-noise processes with interdependence between shock and arrival time," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 15-26.
    2. Søren Asmussen & Romain Biard, 2011. "Ruin probabilities for a regenerative Poisson gap generated risk process," Post-Print hal-00569254, HAL.
    3. Chen, Yiqing & Yuen, Kam C., 2012. "Precise large deviations of aggregate claims in a size-dependent renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 457-461.

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