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Randomized observation periods for the compound Poisson risk model: the discounted penalty function

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  • Hansjörg Albrecher
  • Eric Cheung
  • Stefan Thonhauser

Abstract

In the framework of collective risk theory, we consider a compound Poisson risk model for the surplus process where the process (and hence ruin) can only be observed at random observation times. For Erlang(n) distributed inter-observation times, explicit expressions for the discounted penalty function at ruin are derived. The resulting model contains both the usual continuous-time and the discrete-time risk model as limiting cases, and can be used as an effective approximation scheme for the latter. Numerical examples are given that illustrate the effect of random observation times on various ruin-related quantities.

Suggested Citation

  • Hansjörg Albrecher & Eric Cheung & Stefan Thonhauser, 2013. "Randomized observation periods for the compound Poisson risk model: the discounted penalty function," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2013(6), pages 424-452.
    • Handle: RePEc:taf:sactxx:v:2013:y:2013:i:6:p:424-452
    DOI: 10.1080/03461238.2011.624686
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    Cited by:

    1. Jos'e Miguel Flores-Contr'o & S'everine Arnold, 2023. "The Role of Direct Capital Cash Transfers Towards Poverty and Extreme Poverty Alleviation -- An Omega Risk Process," Papers 2401.06141, arXiv.org, revised Feb 2024.
    2. Teng, Ye & Zhang, Zhimin, 2023. "On a time-changed Lévy risk model with capital injections and periodic observation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 290-314.

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