Optimal mean-variance investment and reinsurance with a correlation under Heston’s SV model

This article investigates the optimal investment and reinsurance problem under the interdependence between the risk assets invested and insurers’ surplus process. Expressly, we consider the price process is described by Heston’s stochastic volatility model and the interdependence between the financial market and the insurance market described by the Wiener processes in models. For the optimal control problem of a nonlinear stochastic differential equation, a novel value function is established to solve the complex Hamilton-Jacobi-Bellman equation. The closed-form expressions of the optimal strategies and the corresponding value function for this new problem are given under the mean-variance criterion. Finally, a numerical simulation example is provided to the impact of correlation on results and providing a reasonable economic explanation.