Robust time-consistent reinsurance-investment strategy with model uncertainty under 4/2 stochastic volatility model

Hao Chang and Zhen Chen

Scandinavian Actuarial Journal, 2025, vol. 2025, issue 6, 574-597

Abstract: This paper examines the robust time-consistent reinsurance-investment strategy for an ambiguity-averse insurer under the 4/2 stochastic volatility model. In this model, an ambiguity-averse insurer transfers the risk generated by insurance claims through purchasing proportional reinsurance and invests the remaining capital in a financial market composed of a risk-free and a risky asset to manage the risk. The claim process is described by the classical Cramér-Lundberg process, while the price process of the risky asset is driven by the 4/2 stochastic volatility model. Under the mean-variance criterion, by employing the stochastic optimal control theory, we establish the corresponding extended Hamilton-Jacobi-Bellman (HJB) equation, and derive the robust time-consistent reinsurance-investment strategy and the corresponding equilibrium value function. In addition, we also study the reinsurance-investment problem in the case of excess-of-loss reinsurance. Finally, a sensitivity analysis is given to examine the results obtained.

Date: 2025
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DOI: 10.1080/03461238.2024.2443849

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