A non-zero-sum stochastic differential game between two mean-variance insurers with inside information

This paper is devoted to the study of a non-zero-sum investment-reinsurance game between two insurers with different opinions about some inside information. Each insurer is concerned about her terminal wealth level and the relative performance of wealth. We assume that the surplus processes of the insurers are correlated jump-diffusion processes. The insurers can invest in the financial market consisting of a risk-free asset and a risky asset. From the beginning of the transaction, the insurers have some inside information about the risky asset price in the future, which is disturbed by noise. However, one insurer trusts it while the other does not. We use the filtration expansion technique to transform the wealth processes for these two insurers with inside information. Then, under the dynamic mean-variance criterion, the explicit solutions for the equilibrium investment-reinsurance strategy and the equilibrium value function are derived by solving the extended HJB equations. Finally, the numerical examples are provided to analyze the effects of the inside information and the model parameters on the equilibrium strategy and the effective frontier.