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Worst‐Case Investment and Reinsurance Optimization for an Insurer under Model Uncertainty

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  • Xiangbo Meng
  • Ximin Rong
  • Lidong Zhang
  • Ziping Du

Abstract

In this paper, we study optimal investment‐reinsurance strategies for an insurer who faces model uncertainty. The insurer is allowed to acquire new business and invest into a financial market which consists of one risk‐free asset and one risky asset whose price process is modeled by a Geometric Brownian motion. Minimizing the expected quadratic distance of the terminal wealth to a given benchmark under the “worst‐case” scenario, we obtain the closed‐form expressions of optimal strategies and the corresponding value function by solving the Hamilton‐Jacobi‐Bellman (HJB) equation. Numerical examples are presented to show the impact of model parameters on the optimal strategies.

Suggested Citation

  • Xiangbo Meng & Ximin Rong & Lidong Zhang & Ziping Du, 2016. "Worst‐Case Investment and Reinsurance Optimization for an Insurer under Model Uncertainty," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:9693419
    DOI: 10.1155/2016/9693419
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    References listed on IDEAS

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    1. Lihua Bai & Huayue Zhang, 2008. "Dynamic mean-variance problem with constrained risk control for the insurers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 181-205, August.
    2. Sid Browne, 1995. "Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 937-958, November.
    3. Zhang, Xin & Siu, Tak Kuen, 2009. "Optimal investment and reinsurance of an insurer with model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 81-88, August.
    4. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
    5. Denis Talay & Ziyu Zheng, 2002. "Worst case model risk management," Finance and Stochastics, Springer, vol. 6(4), pages 517-537.
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