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Ruin probabilities for a regenerative Poisson gap generated risk process

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Author Info

  • Søren Asmussen

    ()
    (Department of Mathematical Sciences - Aarhus University)

  • Romain Biard

    ()
    (Department of Mathematical Sciences - Aarhus University)

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    Abstract

    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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    File URL: http://hal.archives-ouvertes.fr/docs/00/58/82/69/PDF/sarbHAL2.pdf
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    Bibliographic Info

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

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    Date of creation: 2011
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    Publication status: Published, European Actuarial Journal, 2011, 1, 1, 3-22
    Handle: RePEc:hal:journl:hal-00569254

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00569254/en/
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    Related research

    Keywords: Ruin theory ; Subexponential distribution ; Large deviations ; Markov additive process ; Finite horizon ruin;

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    References

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    1. 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.
    2. 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.
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    Cited by:
    1. Dominik Kortschak & Stéphane Loisel & Pierre Ribereau, 2014. "Ruin problems with worsening risks or with infinite mean claims," Post-Print hal-00735843, HAL.
    2. repec:hal:wpaper:hal-00735843 is not listed on IDEAS
    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.
    4. 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.

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