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On the expected discounted penalty function for a risk model with dependence under a multi-layer dividend strategy

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  • Jie-Hua Xie
  • Wei Zou

Abstract

In this article, we consider a dependent risk model in the presence of a multi-laydividend strategy. We construct the dependence structure between the claim size and interclaim time by a Farlie–Gumbel–Morgenstern copula. A piecewise integro-differential equations for the expected discounted penalty function with boundary conditions are established. A renewal equation satisfied by the expected discounted penalty function is obtained via the translation operator. Then, we provide a recursive approach to derive the analytical solution of the expected discounted penalty function. Finally, a numerical example is presented to illustrate the solution procedure.

Suggested Citation

  • Jie-Hua Xie & Wei Zou, 2017. "On the expected discounted penalty function for a risk model with dependence under a multi-layer dividend strategy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(4), pages 1898-1915, February.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:4:p:1898-1915
    DOI: 10.1080/03610926.2015.1030424
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    Cited by:

    1. He, Yue & Kawai, Reiichiro & Shimizu, Yasutaka & Yamazaki, Kazutoshi, 2023. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 1-28.
    2. Olena Ragulina & Jonas Šiaulys, 2020. "Upper Bounds and Explicit Formulas for the Ruin Probability in the Risk Model with Stochastic Premiums and a Multi-Layer Dividend Strategy," Mathematics, MDPI, vol. 8(11), pages 1-35, October.
    3. Yue He & Reiichiro Kawai & Yasutaka Shimizu & Kazutoshi Yamazaki, 2022. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Papers 2203.10680, arXiv.org, revised Dec 2022.

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