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Optimal time-consistent investment and reinsurance strategies for mean–variance insurers with state dependent risk aversion

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  • Li, Yongwu
  • Li, Zhongfei

Abstract

In this paper, we study an insurer’s optimal time-consistent strategies under the mean–variance criterion with state dependent risk aversion. It is assumed that the surplus process is approximated by a diffusion process. The insurer can purchase proportional reinsurance and invest in a financial market which consists of one risk-free asset and multiple risky assets whose price processes follow geometric Brownian motions. Under these, we consider two optimization problems, an investment–reinsurance problem and an investment-only problem. In particular, when the risk aversion depends dynamically on current wealth, the model is more realistic. Using the approach developed by Björk and Murgoci (2009), the optimal time-consistent strategies for the two problems are derived by means of corresponding extension of the Hamilton–Jacobi–Bellman equation. The optimal time-consistent strategies are dependent on current wealth, this case thus is more reasonable than the one with constant risk aversion.

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  • Li, Yongwu & Li, Zhongfei, 2013. "Optimal time-consistent investment and reinsurance strategies for mean–variance insurers with state dependent risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 86-97.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:86-97
    DOI: 10.1016/j.insmatheco.2013.03.008
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    11. Caibin Zhang & Zhibin Liang & Kam Chuen Yuen, 2019. "Optimal dynamic reinsurance with common shock dependence and state-dependent risk aversion," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-45, March.
    12. Alia, Ishak & Chighoub, Farid & Sohail, Ayesha, 2016. "A characterization of equilibrium strategies in continuous-time mean–variance problems for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 212-223.
    13. Yang Shen & Bin Zou, 2021. "Mean-Variance Investment and Risk Control Strategies -- A Time-Consistent Approach via A Forward Auxiliary Process," Papers 2101.03954, arXiv.org.
    14. Liang, Zongxia & Song, Min, 2015. "Time-consistent reinsurance and investment strategies for mean–variance insurer under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 66-76.
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