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Optimal dividend problem for a generalized compound Poisson risk model

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  • Chuancun Yin

Abstract

In this note we study the optimal dividend problem for a company whose surplus process, in the absence of dividend payments, evolves as a generalized compound Poisson model in which the counting process is a generalized Poisson process. This model including the classical risk model and the Polya-Aeppli risk model as special cases. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that under some conditions the optimal dividend strategy is formed by a barrier strategy.

Suggested Citation

  • Chuancun Yin, 2013. "Optimal dividend problem for a generalized compound Poisson risk model," Papers 1305.1747, arXiv.org, revised Feb 2014.
    • Handle: RePEc:arx:papers:1305.1747
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    References listed on IDEAS

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    1. Florin Avram & Zbigniew Palmowski & Martijn R. Pistorius, 2007. "On the optimal dividend problem for a spectrally negative L\'{e}vy process," Papers math/0702893, arXiv.org.
    2. Dickson, D. C. M., 2001. "Lundberg Approximations for Compound Distributions with Insurance Applications. By G. E. Willmot and X. S. Lin. (Springer, 2000)," British Actuarial Journal, Cambridge University Press, vol. 7(4), pages 690-691, October.
    3. Pablo Azcue & Nora Muler, 2005. "Optimal Reinsurance And Dividend Distribution Policies In The Cramér‐Lundberg Model," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 261-308, April.
    4. Albrecher, Hansjörg & Thonhauser, Stefan, 2008. "Optimal dividend strategies for a risk process under force of interest," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 134-149, August.
    5. Pablo Azcue & Nora Muler, 2010. "Optimal investment policy and dividend payment strategy in an insurance company," Papers 1010.4988, arXiv.org.
    6. Hansen, B. G. & Willekens, E., 1990. "The generalized logarithmic series distribution," Statistics & Probability Letters, Elsevier, vol. 9(4), pages 311-316, April.
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    Cited by:

    1. Zhang, Huiming & Liu, Yunxiao & Li, Bo, 2014. "Notes on discrete compound Poisson model with applications to risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 325-336.

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