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Ruin probabilities for a regenerative Poisson gap generated risk process

Listed author(s):
  • Søren Asmussen


    (Department of Mathematical Sciences - Aarhus University)

  • Romain Biard


    (Department of Mathematical Sciences - Aarhus University)

Registered author(s):

    A risk process with constant premium rate $c$ and Poisson arrivals of claims is considered. A threshold $r$ is defined for claim interarrival times, such that if $k$ consecutive interarrival times are larger than $r$, then the next claim has distribution $G$. Otherwise, the claim size distribution is $F$. Asymptotic expressions for the infinite horizon ruin probabilities are given for both light- and the heavy-tailed cases. A basic observation is that the process regenerates at each $G$-claim. Also an approach via Markov additive processes is outlined, and heuristics are given for the distribution of the time to ruin.

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    Paper provided by HAL in its series Post-Print with number hal-00569254.

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    Date of creation: 2011
    Publication status: Published in European Actuarial Journal, 2011, 1 (1), pp.3-22. <10.1007/s13385-011-0002-8>
    Handle: RePEc:hal:journl:hal-00569254
    DOI: 10.1007/s13385-011-0002-8
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    1. Albrecher, Hansjorg & Boxma, Onno J., 2004. "A ruin model with dependence between claim sizes and claim intervals," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 245-254, October.
    2. 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.
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