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Optimal robust reinsurance-investment strategies for insurers with mean reversion and mispricing

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  • Gu, Ailing
  • Viens, Frederi G.
  • Yao, Haixiang

Abstract

This paper considers how to optimize reinsurance and investment decisions for an insurer who has aversion to model ambiguity, who wants to take into consideration time-varying investment conditions via mean reverting models, and who wants to take advantage of statistical arbitrage opportunities afforded by mispricing of stocks. We work under a complex realistic environment: The surplus process is described by a jump–diffusion model and the financial market contains a market index, a risk-free asset, and a pair of mispriced stocks, where the expected return rate of the stocks and the mispricing follow mean reverting stochastic processes which take into account liquidity constraints. The insurer is allowed to purchase reinsurance and to invest in the financial market. We formulate an optimal robust reinsurance-investment problem under the assumption that the insurer is ambiguity-averse to the uncertainty from the financial market and to the uncertainty of the insured’s claims. Ambiguity aversion is an aversion to the uncertainty taken by making investment decisions based on a misspecified model. By employing the dynamic programming approach, we derive explicit formulae for the optimal robust reinsurance-investment strategy and the optimal value function. Numerical examples are presented to illustrate the impact of some parameters on the optimal strategy and on utility loss functions. Among our various practical findings and recommendations, we find that strengthened market liquidity significantly increases the demand for hedging from the mispriced market, to take advantage of the statistical arbitrage it affords.

Suggested Citation

  • Gu, Ailing & Viens, Frederi G. & Yao, Haixiang, 2018. "Optimal robust reinsurance-investment strategies for insurers with mean reversion and mispricing," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 93-109.
  • Handle: RePEc:eee:insuma:v:80:y:2018:i:c:p:93-109
    DOI: 10.1016/j.insmatheco.2018.03.004
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    References listed on IDEAS

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    2. Ning Bin & Huainian Zhu & Chengke Zhang, 2023. "Stochastic Differential Games on Optimal Investment and Reinsurance Strategy with Delay Under the CEV Model," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-27, June.
    3. Zhao, Hui & Shen, Yang & Zeng, Yan & Zhang, Wenjun, 2019. "Robust equilibrium excess-of-loss reinsurance and CDS investment strategies for a mean–variance insurer with ambiguity aversion," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 159-180.
    4. Wang, Hao & Wang, Rongming & Wei, Jiaqin, 2019. "Time-consistent investment-proportional reinsurance strategy with random coefficients for mean–variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 104-114.
    5. Koch-Medina, Pablo & Moreno-Bromberg, Santiago & Ravanelli, Claudia & Šikić, Mario, 2021. "Revisiting optimal investment strategies of value-maximizing insurance firms," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 131-151.
    6. Guerra, M. & de Moura, A.B., 2021. "Reinsurance of multiple risks with generic dependence structures," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 547-571.
    7. Nicole Bauerle & Gregor Leimcke, 2020. "Robust Optimal Investment and Reinsurance Problems with Learning," Papers 2001.11301, arXiv.org.
    8. Sun, Jingyun & Yao, Haixiang & Kang, Zhilin, 2019. "Robust optimal investment–reinsurance strategies for an insurer with multiple dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 157-170.
    9. Zhu, Huainian & Cao, Ming & Zhang, Chengke, 2019. "Time-consistent investment and reinsurance strategies for mean-variance insurers with relative performance concerns under the Heston model," Finance Research Letters, Elsevier, vol. 30(C), pages 280-291.
    10. Liu, Bing & Meng, Hui & Zhou, Ming, 2021. "Optimal investment and reinsurance policies for an insurer with ambiguity aversion," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    11. Guan, Guohui & Hu, Xiang, 2022. "Equilibrium mean–variance reinsurance and investment strategies for a general insurance company under smooth ambiguity," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    12. Guan, Guohui & Liang, Zongxia & Feng, Jian, 2018. "Time-consistent proportional reinsurance and investment strategies under ambiguous environment," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 122-133.
    13. Guan, Guohui & Liang, Zongxia, 2019. "Robust optimal reinsurance and investment strategies for an AAI with multiple risks," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 63-78.

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