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Dividend problems in the dual risk model with exponentially distributed observation time

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  • Peng, Dan
  • Liu, Donghai
  • Liu, Zaiming

Abstract

In this paper, we consider the dual of the compound Poisson risk model with exponentially distributed observation time and constant dividend barrier strategy. We derive and solve the integro-differential equations satisfied by the expected total discounted dividend payments until ruin and ruin probability when the gains follow an exponential distribution. Moreover, numerical illustrations for the effect of random observation time on the expected value of the discounted sum of all dividend payments until ruin and ruin probability are studied.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:3:p:841-849
    DOI: 10.1016/j.spl.2012.11.025
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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. Sheldon Lin, X. & E. Willmot, Gordon & Drekic, Steve, 2003. "The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 551-566, December.
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    Cited by:

    1. 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).
    2. Zailei Cheng, 2017. "Optimal dividends in the dual risk model under a stochastic interest rate," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-16, March.
    3. Zailei Cheng, 2017. "Optimal Dividends in the Dual Risk Model under a Stochastic Interest Rate," Papers 1705.08411, arXiv.org.
    4. 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.

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