Equilibrium analysis in a multi-agent reinsurance chain

2026-07-17

AI Summary

This study investigates strategic interactions and competitive equilibrium within a multi-layer reinsurance chain comprising m insurers and n reinsurers. A stochastic differential game framework is developed, wherein Stackelberg games model hierarchical reinsurance relationships across layers, non-zero-sum games capture inter-insurer competition, and investment in both risky and risk-free assets is incorporated. Under the mean-variance criterion, explicit equilibrium strategies are derived for the first time for both proportional and excess-of-loss reinsurance contracts, revealing how intensified market competition exerts downward pressure on safety loading rates. By solving an extended system of Hamilton–Jacobi–Bellman (HJB) equations and conducting numerical experiments, the analysis demonstrates that heightened competition among insurers significantly reduces safety loadings across all reinsurance layers.

Abstract

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.

Problem

• reinsurance chain
• Stackelberg differential game
• non-zero-sum game
• equilibrium analysis
• stochastic differential game

Innovation

• Stackelberg differential game
• multi-layer reinsurance chain
• mean-variance criterion
• extended HJB system
• non-zero-sum game