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Ruin probabilities and aggregrate claims distributions for shot noise Cox processes

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  • Hansjörg Albrecher
  • Søren Asmussen c

Abstract

We consider a risk process R t where the claim arrival process is a superposition of a homogeneous Poisson process and a Cox process with a Poisson shot noise intensity process, capturing the effect of sudden increases of the claim intensity due to external events. The distribution of the aggregate claim size is investigated under these assumptions. For both light-tailed and heavy-tailed claim size distributions, asymptotic estimates for infinite-time and finite-time ruin probabilities are derived. Moreover, we discuss an extension of the model to an adaptive premium rule that is dynamically adjusted according to past claims experience.

Suggested Citation

  • Hansjörg Albrecher & Søren Asmussen c, 2006. "Ruin probabilities and aggregrate claims distributions for shot noise Cox processes," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2006(2), pages 86-110.
    • Handle: RePEc:taf:sactxx:v:2006:y:2006:i:2:p:86-110
    DOI: 10.1080/03461230600630395
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    Cited by:

    1. Teng, Ye & Zhang, Zhimin, 2023. "Finite-time expected present value of operating costs until ruin in a Cox risk model with periodic observation," Applied Mathematics and Computation, Elsevier, vol. 452(C).
    2. Simon Pojer & Stefan Thonhauser, 2023. "The Markovian Shot-noise Risk Model: A Numerical Method for Gerber-Shiu Functions," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    3. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2023. "Optimal dividend strategies for a catastrophe insurer," Papers 2311.05781, arXiv.org.

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