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Ruin probabilities for a regenerative Poisson gap generated risk process

Author

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  • Søren Asmussen

    (Department of Mathematical Sciences - Aarhus University [Aarhus])

  • Romain Biard

    (Department of Mathematical Sciences - Aarhus University [Aarhus])

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.

Suggested Citation

  • Søren Asmussen & Romain Biard, 2011. "Ruin probabilities for a regenerative Poisson gap generated risk process," Post-Print hal-00569254, HAL.
    • Handle: RePEc:hal:journl:hal-00569254
    DOI: 10.1007/s13385-011-0002-8
    Note: View the original document on HAL open archive server: https://hal.science/hal-00569254v2
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    References listed on IDEAS

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    1. Asmussen, Søren & Klüppelberg, Claudia, 1996. "Large deviations results for subexponential tails, with applications to insurance risk," Stochastic Processes and their Applications, Elsevier, vol. 64(1), pages 103-125, November.
    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.
    3. 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.
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    1. repec:hal:wpaper:hal-00735843 is not listed on IDEAS
    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.
    4. Dominik Kortschak & Stéphane Loisel & Pierre Ribereau, 2014. "Ruin problems with worsening risks or with infinite mean claims," Post-Print hal-00735843, HAL.

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    More about this item

    Keywords

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