Robust investment and reinsurance strategies under inflation risk and CEV model

Chen Wang; Hongmin Xiao; Chen Wang; Hongmin Xiao

doi:10.3934/math.2025642

AIMS Mathematics

2025, Volume 10, Issue 6: 14248-14277. doi: 10.3934/math.2025642

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Research article

Robust investment and reinsurance strategies under inflation risk and CEV model

Chen Wang ,
Hongmin Xiao ^,

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received: 31 March 2025 Revised: 25 May 2025 Accepted: 25 May 2025 Published: 23 June 2025
MSC : 62P05, 93E20

This paper innovatively investigated the optimal investment and reinsurance problem with the objective of minimizing the probability of insolvency in a framework that simultaneously considers the ambiguity aversion perspective and inflation risk. Different from traditional research, this study assumed that insurance companies can not only purchase proportional reinsurance to minimize claims risk but also invest in the financial market, and examined the impact of inflation on the prices of risky assets through discounting. In particular, we incorporated the inflation effect into the pricing of risky assets and proposed a new investment model that takes inflation into account. The surplus process of an insurance company was modeled using a diffusion approximation model, and the financial market consisted of risk-free assets and risky assets, in which the price of risky assets was described by the constant elasticity of variance (CEV) model, which has an advantage in capturing market volatility compared to traditional models. Through the Radon-Nikodym derivative and Girsanov's theorem, we derived the wealth process of an insurance company from the perspective of ambiguity aversion. Based on the principle of dynamic programming, the HJB equation of the optimization problem was established, and the analytical solutions of the robust optimal investment and reinsurance strategies were obtained. Finally, the sensitivity of the model parameters to the theoretical results was analyzed through numerical simulation experiments, which provides quantitative guidance for insurance company's investment and reinsurance decisions in complex economic environments.
- probability of ruin,
- ambiguity aversion,
- inflation,
- HJB equation,
- robust investment strategy,
- robust reinsurance strategy,
- stochastic optimal control
Citation: Chen Wang, Hongmin Xiao. Robust investment and reinsurance strategies under inflation risk and CEV model[J]. AIMS Mathematics, 2025, 10(6): 14248-14277. doi: 10.3934/math.2025642

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Abstract

This paper innovatively investigated the optimal investment and reinsurance problem with the objective of minimizing the probability of insolvency in a framework that simultaneously considers the ambiguity aversion perspective and inflation risk. Different from traditional research, this study assumed that insurance companies can not only purchase proportional reinsurance to minimize claims risk but also invest in the financial market, and examined the impact of inflation on the prices of risky assets through discounting. In particular, we incorporated the inflation effect into the pricing of risky assets and proposed a new investment model that takes inflation into account. The surplus process of an insurance company was modeled using a diffusion approximation model, and the financial market consisted of risk-free assets and risky assets, in which the price of risky assets was described by the constant elasticity of variance (CEV) model, which has an advantage in capturing market volatility compared to traditional models. Through the Radon-Nikodym derivative and Girsanov's theorem, we derived the wealth process of an insurance company from the perspective of ambiguity aversion. Based on the principle of dynamic programming, the HJB equation of the optimization problem was established, and the analytical solutions of the robust optimal investment and reinsurance strategies were obtained. Finally, the sensitivity of the model parameters to the theoretical results was analyzed through numerical simulation experiments, which provides quantitative guidance for insurance company's investment and reinsurance decisions in complex economic environments.

References

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