IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-00569254.html
   My bibliography  Save this paper

Ruin probabilities for a regenerative Poisson gap generated risk process

Author

Listed:
  • 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.archives-ouvertes.fr/hal-00569254v2
    as

    Download full text from publisher

    File URL: https://hal.archives-ouvertes.fr/hal-00569254v2/document
    Download Restriction: no

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:hal:wpaper:hal-00735843 is not listed on IDEAS
    2. 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.
    3. 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.
    4. Dominik Kortschak & Stéphane Loisel & Pierre Ribereau, 2014. "Ruin problems with worsening risks or with infinite mean claims," Post-Print hal-00735843, HAL.

    More about this item

    Keywords

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-00569254. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.