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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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Author Info

  • Romain Biard

    ()
    (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429)

  • Claude Lefèvre

    ()
    (Département de Mathématique - Université Libre de Bruxelles)

  • Stéphane Loisel

    ()
    (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429)

  • Haikady Nagaraja

    ()
    (Department of Statistics - Ohio State University)

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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Bibliographic Info

Paper provided by HAL in its series Post-Print with number hal-00409418.

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Date of creation: 2011
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Publication status: Published, Applied Stochastic Models in Business and Industry, 2011, 27, 5, 503-518.
Handle: RePEc:hal:journl:hal-00409418

Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00409418
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Web page: http://hal.archives-ouvertes.fr/

Related research

Keywords: Risk process; finite-time ruin probabilities; asymptotic approximation for large initial reserves; path-dependent claims; heavy-tailed claim amounts; Poisson spacing;

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Cited by:
  1. 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.
  2. Li, Xiaohu & Wu, Jintang, 2014. "Asymptotic tail behavior of Poisson shot-noise processes with interdependence between shock and arrival time," Statistics & Probability Letters, Elsevier, Elsevier, vol. 88(C), pages 15-26.
  3. Søren Asmussen & Romain Biard, 2011. "Ruin probabilities for a regenerative Poisson gap generated risk process," Post-Print, HAL hal-00569254, HAL.

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