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Dividends and reinsurance under a penalty for ruin

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  • Liang, Zhibin
  • Young, Virginia R.
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    Abstract

    We find the optimal dividend strategy in a diffusion risk model under a penalty for ruin, as in Thonhauser and Albrecher (2007), although we allow for both a positive and a negative penalty. Furthermore, we determine the optimal proportional reinsurance strategy, when so-called expensive reinsurance is available; that is, the premium loading on reinsurance is greater than the loading on the directly written insurance. One can think of our model as taking the one in Taksar (2000, Section 6) and adding a penalty for ruin.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167668712000212
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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 50 (2012)
    Issue (Month): 3 ()
    Pages: 437-445

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    Handle: RePEc:eee:insuma:v:50:y:2012:i:3:p:437-445

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Optimal dividends; Optimal reinsurance; Ruin; Stochastic optimal control; Legendre dual;

    References

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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, vol. 38(1), pages 57-80, February.
    2. Loeffen, R.L., 2009. "An optimal dividends problem with transaction costs for spectrally negative Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 41-48, August.
    3. Paulsen, Jostein & Gjessing, Hakon K., 1997. "Optimal choice of dividend barriers for a risk process with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 20(3), pages 215-223, October.
    4. Thonhauser, Stefan & Albrecher, Hansjorg, 2007. "Dividend maximization under consideration of the time value of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 163-184, July.
    5. Bjarne H�jgaard & Michael Taksar, 2004. "Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 315-327.
    6. Meng, Hui & Siu, Tak Kuen, 2011. "On optimal reinsurance, dividend and reinvestment strategies," Economic Modelling, Elsevier, vol. 28(1), pages 211-218.
    7. Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 1-15, June.
    8. T. Choulli & M. Taksar & X. Y. Zhou, 2001. "Excess-of-loss reinsurance for a company with debt liability and constraints on risk reduction," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 573-596.
    9. Loeffen, Ronnie L. & Renaud, Jean-François, 2010. "De Finetti's optimal dividends problem with an affine penalty function at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 98-108, February.
    10. Bjarne Højgaard & Søren Asmussen & Michael Taksar, 2000. "Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation," Finance and Stochastics, Springer, vol. 4(3), pages 299-324.
    11. Yao, Dingjun & Yang, Hailiang & Wang, Rongming, 2011. "Optimal dividend and capital injection problem in the dual model with proportional and fixed transaction costs," European Journal of Operational Research, Elsevier, vol. 211(3), pages 568-576, June.
    12. 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.
    13. Kulenko, Natalie & Schmidli, Hanspeter, 2008. "Optimal dividend strategies in a Cramér-Lundberg model with capital injections," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 270-278, October.
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    Cited by:
    1. Yao, Dingjun & Yang, Hailiang & Wang, Rongming, 2014. "Optimal risk and dividend control problem with fixed costs and salvage value: Variance premium principle," Economic Modelling, Elsevier, vol. 37(C), pages 53-64.

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