Robust Stochastic Differential Proportional Reinsurance Games with Heterogeneous Insurers

This article examines a stochastic differential proportional reinsurance game under model uncertainty, framed within a Stackelberg game where one reinsurer and n insurers, all assumed to be ambiguity-averse, interact. The reinsurer, acting as the leader, seeks to maximize the expected utility of the combined terminal wealth of all players, rather than its own utility. The reinsurer controls risk pooling and determines insurers’ risk quotas through risk adjustment coefficients. The insurers, in turn, manage their risks and expand their underwriting capacity by purchasing reinsurance and adopting strategies based on relative performance in a non-zero-sum stochastic differential game. Using dynamic programming and backward induction, we derive explicit expressions for the robust equilibrium strategies. Through numerical simulations, the article presents a comparative static analysis of the equilibrium strategies. The results show that the risk adjustment coefficient is positively correlated with the reinsurance premium and negatively correlated with the reinsurance ratio. As business correlation increases, the reinsurer reallocates a more significant portion of the risk quota to the lower risk insurer, optimizing risk distribution and improving overall portfolio management. Additionally, we observe that higher ambiguity aversion leads to more conservative reinsurance strategies, which in turn affect the reinsurer’s premium-setting behavior.