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Dividend Problems in the Diffusion Model with Interest and Exponentially Distributed Observation Time

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  • Cuilian Wang
  • Xiao Liu

Abstract

Consider dividend problems in the diffusion model with interest 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 level, the excess is paid as dividend. In this paper, integrodifferential equations for the moment‐generating function, the nth moment function, and the Laplace transform of ruin time are derived; explicit expressions for the expected discounted dividends paid until ruin and the Laplace transform of ruin time are also obtained.

Suggested Citation

  • Cuilian Wang & Xiao Liu, 2014. "Dividend Problems in the Diffusion Model with Interest and Exponentially Distributed Observation Time," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:814835
    DOI: 10.1155/2014/814835
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    References listed on IDEAS

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    1. Hansjörg Albrecher & Eric Cheung & Stefan Thonhauser, 2013. "Randomized observation periods for the compound Poisson risk model: the discounted penalty function," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2013(6), pages 424-452.
    2. 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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