A class of non-zero-sum stochastic differential games between two mean-variance insurers under stochastic volatility

Abstract

This paper studies the open-loop equilibrium strategies for a class of non-zero-sum reinsurance-investment stochastic differential games between two insurers with a state-dependent mean expectation in the incomplete market. Both insurers are able to purchase proportional reinsurance contracts and invest their wealth in a risk-free asset and a risky asset whose price is modeled by a general stochastic volatility model. The surplus processes of two insurers are driven by two standard Brownian motions. The objective for each insurer is to find the equilibrium investment and reinsurance strategies to balance the expected return and variance of relative terminal wealth. Incorporating the forward ..