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

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.