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On optimal reinsurance, dividend and reinvestment strategies

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  • Meng, Hui
  • Siu, Tak Kuen

Abstract

We investigate an optimal reinsurance and dividend problem of an insurance company with the presence of reinvestments, or retained earnings. We consider the general situation that the company needs to pay both fixed and proportional costs. The object of the company is to determine reinsurance, dividend and reinvestment strategies so as to maximize the difference between the expected discounted dividends minus the expected discounted reinvestment until the time of ruin. We focus on the excess-of-loss reinsurance strategy, which is shown to be optimal. The mixed classical-impulse control is then used to discuss the problem. Using inventory control theory, the value function and optimal strategy are derived.

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Bibliographic Info

Article provided by Elsevier in its journal Economic Modelling.

Volume (Year): 28 (2011)
Issue (Month): 1-2 (January)
Pages: 211-218

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Handle: RePEc:eee:ecmode:v:28:y:2011:i:1-2:p:211-218

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Web page: http://www.elsevier.com/locate/inca/30411

Related research

Keywords: Reinvestment Reinsurance Dividend Excess-of-loss Impulse control Transaction costs;

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References

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  1. de Lourdes Centeno, Maria, 2005. "Dependent risks and excess of loss reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 229-238, October.
  2. 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.
  3. Paulsen, Jostein & Gjessing, Hakon, 1994. "Properties of functions of the excess of loss retention limit with applications," Insurance: Mathematics and Economics, Elsevier, vol. 15(1), pages 1-21, October.
  4. Gerber, Hans U. & Smith, Nathaniel, 2008. "Optimal dividends with incomplete information in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 227-233, October.
  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. He, Lin & Liang, Zongxia, 2009. "Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 88-94, February.
  7. Løkka, Arne & Zervos, Mihail, 2008. "Optimal dividend and issuance of equity policies in the presence of proportional costs," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 954-961, June.
  8. He, Lin & Liang, Zongxia, 2008. "Optimal financing and dividend control of the insurance company with proportional reinsurance policy," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 976-983, June.
  9. 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.
  10. 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.
  11. Irgens, Christian & Paulsen, Jostein, 2004. "Optimal control of risk exposure, reinsurance and investments for insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 21-51, August.
  12. 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.
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Citations

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Cited by:
  1. Guan, Huiqi & Liang, Zongxia, 2014. "Viscosity solution and impulse control of the diffusion model with reinsurance and fixed transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 109-122.
  2. 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.
  3. Chen, Mi & Peng, Xiaofan & Guo, Junyi, 2013. "Optimal dividend problem with a nonlinear regular-singular stochastic control," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 448-456.
  4. Liang, Zhibin & Young, Virginia R., 2012. "Dividends and reinsurance under a penalty for ruin," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 437-445.

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