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Optimal Dividend and reinsurance strategy of a Property Insurance Company under Catastrophe Risk

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  • Zongxia Liang
  • Lin He
  • Jiaoling Wu

Abstract

We consider an optimal control problem of a property insurance company with proportional reinsurance strategy. The insurance business brings in catastrophe risk, such as earthquake and flood. The catastrophe risk could be partly reduced by reinsurance. The management of the company controls the reinsurance rate and dividend payments process to maximize the expected present value of the dividends before bankruptcy. This is the first time to consider the catastrophe risk in property insurance model, which is more realistic. We establish the solution of the problem by the mixed singular-regular control of jump diffusions. We first derive the optimal retention ratio, the optimal dividend payments level, the optimal return function and the optimal control strategy of the property insurance company, then the impacts of the catastrophe risk and key model parameters on the optimal return function and the optimal control strategy of the company are discussed.

Suggested Citation

  • Zongxia Liang & Lin He & Jiaoling Wu, 2010. "Optimal Dividend and reinsurance strategy of a Property Insurance Company under Catastrophe Risk," Papers 1009.1269, arXiv.org.
    • Handle: RePEc:arx:papers:1009.1269
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    References listed on IDEAS

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    1. Hojgaard, Bjarne & Taksar, Michael, 1998. "Optimal proportional reinsurance policies for diffusion models with transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 41-51, May.
    2. 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.
    3. Bjarne Højgaard & Michael Taksar, 2001. "Optimal risk control for a large corporation in the presence of returns on investments," Finance and Stochastics, Springer, vol. 5(4), pages 527-547.
    4. 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.
    5. He, Lin & Hou, Ping & Liang, Zongxia, 2008. "Optimal control of the insurance company with proportional reinsurance policy under solvency constraints," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 474-479, December.
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    Cited by:

    1. Thilini Mahanama & Abootaleb Shirvani & Svetlozar Rachev, 2022. "A Natural Disasters Index," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 24(2), pages 263-284, April.
    2. Thilini V. Mahanama & Abootaleb Shirvani, 2020. "A Natural Disasters Index," Papers 2008.03672, arXiv.org.

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