Abstract:

This paper studies the optimal reinsurance-investment problem of an insurer and a reinsurer under Heston's stochastic volatility model in the framework of Stackelberg stochastic differential game. We assume that the insurer purchases proportional reinsurance to transfer part of the risk to the reinsurer, and the reinsurer accepts the transferred risk and chooses an appropriate reinsurance premium strategy. At the same time, the insurer and the reinsurer can also invest their surplus in risk-free assets and Heston's stochastic volatility risk model. Under the criterion of maximizing the expected mean-variance utility of terminal wealth, the corresponding extended Hamilton-Jacobi-Bellman equations are developed using stochastic control theory, and verification theorems are given. We obtain specific forms for the equilibrium strategy and the value function. Finally, we analyze the effects of the model parameters on the equilibrium strategies through numerical simulations.

Key words: mean-variance criterion, reinsurance and investment strategy, Heston's SV, Stackelberg stochastic differential game, extended Hamilton-Jacobi-Bellman equation