Research on the Multi-party Hybrid Game of Investment and Reinsurance Influenced by a Large Investor

This article investigates a hybrid investment-reinsurance game between a reinsurer and two insurers. All players invest in a financial market with one risk-free and one risky asset, whose return is affected by the large investor. Given the enormous asset scale, we assume the reinsurer acts as the large investor. As the leader in the Stackelberg game, the reinsurer collects reinsurance premiums. The insurers, as followers, can purchase proportional reinsurance to diversify claim risks. Taking market competition into account, the insurers aim to maximize their relative performance at the terminal time, while the reinsurer seeks to maximize its own expected terminal utility. Using the dynamic programming and the backward induction method, we derive the equilibrium strategies, value functions, and provide a verification theorem. Subsequently, we present relevant conclusions based on several simplified scenarios. Finally, numerical simulations and sensitivity analysis are conducted to illustrate the impact of model parameters on the equilibrium strategies. Key findings: (1) the investment behavior of the reinsurer may either restrain or encourage investment in the risky asset by the participants; (2) the optimal reinsurance strategies depend on the optimal reinsurance premium strategy; (3) the reinsurance strategies of the two insurers interact and exhibit herd behavior.