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On the compound Poisson risk model with dependence and a threshold dividend strategy

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  • Shi, Yafeng
  • Liu, Peng
  • Zhang, Chunsheng

Abstract

In this paper, we consider the compound Poisson risk model with a threshold dividend strategy and a dependence structure modeled by a Farlie–Gumbel–Morgenstern copula. The integro-differential equations satisfied by the Gerber–Shiu functions and the expected discounted dividend payments paid until ruin respectively are derived. Further, by deriving and solving the renewal equations satisfied by the Gerber–Shiu functions and the expected discounted dividend payments, we give the explicit formulas for them.

Suggested Citation

  • Shi, Yafeng & Liu, Peng & Zhang, Chunsheng, 2013. "On the compound Poisson risk model with dependence and a threshold dividend strategy," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 1998-2006.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:9:p:1998-2006
    DOI: 10.1016/j.spl.2013.05.008
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    References listed on IDEAS

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    1. Lin, X.Sheldon & Pavlova, Kristina P., 2006. "The compound Poisson risk model with a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 57-80, February.
    2. Li, Shuanming & Garrido, Jose, 2004. "On a class of renewal risk models with a constant dividend barrier," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 691-701, December.
    3. Landriault, David, 2008. "Constant dividend barrier in a risk model with interclaim-dependent claim sizes," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 31-38, February.
    4. Hans Gerber & Elias Shiu, 2006. "On Optimal Dividend Strategies In The Compound Poisson Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 76-93.
    5. 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.
    6. Yang, Hu & Zhang, Zhimin, 2008. "Gerber-Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 984-991, June.
    7. Sheldon Lin, X. & E. Willmot, Gordon & Drekic, Steve, 2003. "The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 551-566, December.
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    Cited by:

    1. 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.

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