Abstract

In this paper, we investigate the optimal weighted reinsurance contract from the perspective of reinsurance demand and supply within the framework of the Stackelberg-Nash differential game, where both the insurer and reinsurer are allowed to choose their preferred retention levels and reinsurance premiums by negotiation. The ultimate reinsurance contract is established through their optimal strategies and bargaining powers. Assume that both the insurer and reinsurer aim to maximize the expected utility of their terminal wealth. Based on game theory and the dynamic programming approach, we derive the explicit Stackelberg-Nash equilibrium strategies. To gain a deeper understanding of the impact of bargaining powers on the optimal reinsurance contract, we also explore three degenerate optimization problems. Our findings reveal that to successfully secure a reinsurance contract, the negotiation powers of the insurer and the reinsurer cannot be excessively imbalanced. Furthermore, under some specific conditions, this weighted reinsurance contract benefits both parties, constituting a win-win game. Some other theoretical analyses and numerical examples are provided to show the economic intuition and insights of the results.