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Dividend problems in the dual model with diffusion and exponentially distributed observation time

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  • Liu, Xiao
  • Chen, Zhenlong

Abstract

Consider dividend problems in the dual model with diffusion and exponentially distributed observation time where dividends are paid according to a barrier strategy. Assume that dividends can only be paid with a certain probability at each point of time, that is, on each observation, if the surplus exceeds the barrier, the excess is paid as dividend. In this paper, integro-differential equations for the expected discounted sum of dividends paid until ruin and the Laplace transform of ruin time are derived. When the gains are exponentially distributed, explicit expressions for the ruin probability, the expected discounted sum of dividends paid until ruin, the Laplace transform of ruin time and the expectation of ruin time are also obtained.

Suggested Citation

  • Liu, Xiao & Chen, Zhenlong, 2014. "Dividend problems in the dual model with diffusion and exponentially distributed observation time," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 175-183.
    • Handle: RePEc:eee:stapro:v:87:y:2014:i:c:p:175-183
    DOI: 10.1016/j.spl.2014.01.017
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    References listed on IDEAS

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    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. Avanzi, Benjamin & Gerber, Hans U., 2008. "Optimal Dividends in the Dual Model with Diffusion," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 653-667, November.
    3. Peng, Dan & Liu, Donghai & Liu, Zaiming, 2013. "Dividend problems in the dual risk model with exponentially distributed observation time," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 841-849.
    4. 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.
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    Keywords

    Dividend; Ruin; Barrier strategy;
    All these keywords.

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