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Gerber-Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy

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  • Yang, Hu
  • Zhang, Zhimin

Abstract

This paper studies a Sparre Andersen model in which the inter-claim times are generalized Erlang(n) distributed. We assume that the premium rate is a step function depending on the current surplus level. A piecewise integro-differential equation for the Gerber-Shiu discounted penalty function is derived and solved. Finally, to illustrate the solution procedure, explicit expression for the Laplace transform of the time to ruin is given when the inter-claim times are generalized Erlang(2) distributed and the claim amounts are exponentially distributed.

Suggested Citation

  • Yang, Hu & Zhang, Zhimin, 2008. "Gerber-Shiu discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 984-991, June.
  • Handle: RePEc:eee:insuma:v:42:y:2008:i:3:p:984-991
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    References listed on IDEAS

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    1. Lin, X.Sheldon & Pavlova, Kristina P., 2006. "The compound Poisson risk model with a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, pages 57-80.
    2. Li, Shuanming & Garrido, Jose, 2004. "On a class of renewal risk models with a constant dividend barrier," Insurance: Mathematics and Economics, Elsevier, pages 691-701.
    3. Lin, X. Sheldon & Sendova, Kristina P., 2008. "The compound Poisson risk model with multiple thresholds," Insurance: Mathematics and Economics, Elsevier, pages 617-627.
    4. Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, pages 1-15.
    5. Li, Shuanming & Garrido, Jose, 2004. "On ruin for the Erlang(n) risk process," Insurance: Mathematics and Economics, Elsevier, pages 391-408.
    6. Lin, X. Sheldon & Willmot, Gordon E., 1999. "Analysis of a defective renewal equation arising in ruin theory," Insurance: Mathematics and Economics, Elsevier, pages 63-84.
    7. Albrecher, Hansjorg & Claramunt, M.Merce & Marmol, Maite, 2005. "On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times," Insurance: Mathematics and Economics, Elsevier, pages 324-334.
    8. Albrecher, Hansjörg & Hartinger, Jürgen & Thonhauser, Stefan, 2007. "On Exact Solutions for Dividend Strategies of Threshold and Linear Barrier Type in a Sparre Andersen Model," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 37(02), pages 203-233, November.
    9. Dickson, David C. M. & Hipp, Christian, 2001. "On the time to ruin for Erlang(2) risk processes," Insurance: Mathematics and Economics, Elsevier, pages 333-344.
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    Cited by:

    1. Mitric, Ilie-Radu & Sendova, Kristina P. & Tsai, Cary Chi-Liang, 2010. "On a multi-threshold compound Poisson process perturbed by diffusion," Statistics & Probability Letters, Elsevier, pages 366-375.
    2. Jiang, Wuyuan & Yang, Zhaojun & Li, Xinping, 2012. "The discounted penalty function with multi-layer dividend strategy in the phase-type risk model," Statistics & Probability Letters, Elsevier, pages 1358-1366.
    3. Deng, Chao & Zhou, Jieming & Deng, Yingchun, 2012. "The Gerber–Shiu discounted penalty function in a delayed renewal risk model with multi-layer dividend strategy," Statistics & Probability Letters, Elsevier, pages 1648-1656.
    4. repec:eee:apmaco:v:252:y:2015:i:c:p:273-286 is not listed on IDEAS
    5. Shi, Yafeng & Liu, Peng & Zhang, Chunsheng, 2013. "On the compound Poisson risk model with dependence and a threshold dividend strategy," Statistics & Probability Letters, Elsevier, pages 1998-2006.

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