Equilibrium analysis in a multi-agent reinsurance chain

This paper investigates a multi-layer reinsurance chain within a stochastic differential game framework involving m competing insurers and n reinsurers. Specifically, Stackelberg differential games are employed to characterize the strategic interactions between reinsurance buyers and sellers at each layer of the chain. In addition, a non-zero-sum game model is established to capture the competitive behavior among insurers. Both insurers and reinsurers are allowed to invest in a risk-free asset and a risky asset. To examine the heterogeneity of reinsurance chains under different contract types, the analysis is conducted separately for proportional reinsurance and excess-of-loss reinsurance. By combining dynamic programming and game theory, closed-form equilibrium strategies for investment and reinsurance are derived by solving the extended Hamilton-Jacobi-Bellman (HJB) systems under the mean-variance (MV) criterion. Numerical analysis is conducted to explore the impact of key parameters on the equilibrium strategies. The results indicate that intensified competition in the insurance market leads to a reduction in the safety loadings of reinsurance contracts at each layer of the reinsurance chain.