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

Author

Listed:
  • Romain Biard

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Claude Lefèvre

    (ULB - Département de Mathématique [Bruxelles] - ULB - Faculté des Sciences [Bruxelles] - ULB - Université libre de Bruxelles)

  • Stéphane Loisel

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Haikady Nagaraja

    (Department of Statistics - OSU - Ohio State University [Columbus])

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.

Suggested Citation

  • Romain Biard & Claude Lefèvre & Stéphane Loisel & Haikady Nagaraja, 2011. "Asymptotic Finite-Time Ruin Probabilities for a Class of Path-Dependent Heavy-Tailed Claim Amounts Using Poisson Spacings," Post-Print hal-00409418, HAL.
    • Handle: RePEc:hal:journl:hal-00409418
    DOI: 10.1002/asmb.857
    Note: View the original document on HAL open archive server: https://hal.science/hal-00409418
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    Cited by:

    1. Søren Asmussen & Romain Biard, 2011. "Ruin probabilities for a regenerative Poisson gap generated risk process," Post-Print hal-00569254, HAL.
    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, vol. 88(C), pages 15-26.
    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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