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The compound Poisson risk model under a mixed dividend strategy

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  • Zhang, Zhimin
  • Han, Xiao

Abstract

In this paper, we consider a compound Poisson model under a mixed dividend strategy. The mixed dividend strategy is a combination of threshold dividend strategy and periodic dividend strategy. Given a positive threshold level b > 0, whenever the surplus process attains the level b, dividends will be paid off continuously at a rate α > 0. Furthermore, given a sequence of dividend decision times {Zj}j=1∞, whenever the observed surplus level at Zj is larger than b, the excess value will also be paid off as dividend. We study the expected discounted dividend payments before ruin and the Gerber–Shiu expected discounted penalty function. Some numerical examples are also presented.

Suggested Citation

  • Zhang, Zhimin & Han, Xiao, 2017. "The compound Poisson risk model under a mixed dividend strategy," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 1-12.
    • Handle: RePEc:eee:apmaco:v:315:y:2017:i:c:p:1-12
    DOI: 10.1016/j.amc.2017.07.048
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    References listed on IDEAS

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    1. Avanzi, Benjamin & Cheung, Eric C.K. & Wong, Bernard & Woo, Jae-Kyung, 2013. "On a periodic dividend barrier strategy in the dual model with continuous monitoring of solvency," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 98-113.
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    4. Li, Li, 2015. "Bifurcation and chaos in a discrete physiological control system," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 397-404.
    5. Wan, Ning, 2007. "Dividend payments with a threshold strategy in the compound Poisson risk model perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 509-523, May.
    6. 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.
    7. Zhimin Zhang & Eric C. K. Cheung, 2016. "The Markov Additive Risk Process Under an Erlangized Dividend Barrier Strategy," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 275-306, June.
    8. Albrecher, Hansjörg & Cheung, Eric C.K. & Thonhauser, Stefan, 2011. "Randomized Observation Periods for the Compound Poisson Risk Model: Dividends," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 645-672, November.
    9. Shimizu, Yasutaka & Zhang, Zhimin, 2017. "Estimating Gerber–Shiu functions from discretely observed Lévy driven surplus," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 84-98.
    10. Albrecher, Hansjörg & Hartinger, Jürgen & Thonhauser, Stefan, 2007. "On Exact Solutions for Dividend Strategies of Threshold and Linear Barrier Type in a Sparre Andersen Model," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 203-233, November.
    11. Choi, Michael C.H. & Cheung, Eric C.K., 2014. "On the expected discounted dividends in the Cramér–Lundberg risk model with more frequent ruin monitoring than dividend decisions," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 121-132.
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    Cited by:

    1. Wenguang Yu & Peng Guo & Qi Wang & Guofeng Guan & Qing Yang & Yujuan Huang & Xinliang Yu & Boyi Jin & Chaoran Cui, 2020. "On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model," Mathematics, MDPI, vol. 8(4), pages 1-21, April.
    2. Zan Yu & Lianzeng Zhang, 2024. "Computing the Gerber-Shiu function with interest and a constant dividend barrier by physics-informed neural networks," Papers 2401.04378, arXiv.org.
    3. Zhang, Aili & Li, Shuanming & Wang, Wenyuan, 2023. "A scale function based approach for solving integral-differential equations in insurance risk models," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    4. Liu, Zhang & Chen, Ping & Hu, Yijun, 2020. "On the dual risk model with diffusion under a mixed dividend strategy," Applied Mathematics and Computation, Elsevier, vol. 376(C).

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