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On the optimal dividend problem for a spectrally positive Levy process


  • Chuancun Yin
  • Yuzhen Wen
  • Yongxia Zhao


In this paper we study the optimal dividend problem for a company whose surplus process evolves as a spectrally positive Levy process. This model including the dual model of the classical risk model and the dual model with diffusion as special cases. We assume that dividends are paid to the shareholders according to admissible strategy whose dividend rate is bounded by a constant. 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 the optimal dividend strategy is formed by a threshold strategy.

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  • Chuancun Yin & Yuzhen Wen & Yongxia Zhao, 2013. "On the optimal dividend problem for a spectrally positive Levy process," Papers 1302.2231,, revised Mar 2014.
  • Handle: RePEc:arx:papers:1302.2231

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    References listed on IDEAS

    1. Avanzi, Benjamin & U. Gerber, Hans & S.W. Shiu, Elias, 2007. "Optimal dividends in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 111-123, July.
    2. Bayraktar, Erhan & Kyprianou, Andreas E. & Yamazaki, Kazutoshi, 2013. "On Optimal Dividends In The Dual Model," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 43(03), pages 359-372, September.
    3. repec:spr:compst:v:67:y:2008:i:1:p:21-42 is not listed on IDEAS
    4. Erhan Bayraktar & Masahiko Egami, 2008. "Optimizing venture capital investments in a jump diffusion model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(1), pages 21-42, February.
    5. Bjarne Hø jgaard & Michael Taksar, 1999. "Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 153-182.
    6. repec:spr:compst:v:72:y:2010:i:1:p:129-143 is not listed on IDEAS
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    Cited by:

    1. Chuancun Yin & Kam Chuen Yuen, 2014. "Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs," Papers 1409.0407,
    2. Jos'e-Luis P'erez & Kazutoshi Yamazaki, 2016. "Hybrid continuous and periodic barrier strategies in the dual model: optimality and fluctuation identities," Papers 1612.02444,, revised Jan 2018.
    3. Kazutoshi Yamazaki, 2016. "Optimality of two-parameter strategies in stochastic control," Papers 1605.04995,

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