Reinsurance–investment game between two α-maxmin mean–variance insurers

Abstract

This paper examines a non-zero-sum stochastic differential reinsurance-investment game between two competitive insurers under the α-maximin mean-variance criterion. Both insurers can purchase proportional reinsurance and invest in a financial market consisting of one risk-free asset and one risky asset, and each insurer is concerned with its terminal surplus and relative performance compared to its competitor. The insurers aim to maximize the α-maximin mean-variance utility, which allows them to exhibit different attitudes towards model ambiguity. By solving the extended Hamilton-Jacobi-Bellman (HJB) equations for both insurers, we derive the α-robust equilibrium reinsurance and investment strategies. Finally, several numerical examples are provided to illustrate the impact of some model parameters on the equilibrium strategies.