Stochastic differential investment and reinsurance game between an insurer and a reinsurer under thinning dependence structure

This paper investigates a non-zero-sum stochastic differential investment and reinsurance game between an insurer and a reinsurer. It is assumed that the insurer can purchase proportional reinsurance and the claim businesses between the insurer and the reinsurer are correlated through thinning dependence structure. Besides, both the insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset, in which the two risky assets are supposed to be correlated. The objective of each is to maximize the mean–variance utility of the difference between its terminal wealth and that of its cooperator. By solving the extended Hamilton–Jacobi–Bellman systems within the game theoretic framework, explicit expressions of the optimal time-consistent strategies and value functions of the insurer and the reinsurer are derived, and some comparison results with and without game are obtained as well. Finally, several sensitivity analyses and numerical examples are presented to illustrate the effects of market parameters on the optimal strategies as well as the economic interpretation behind.