PARETO-OPTIMAL REINSURANCE-INVESTMENT STRATEGIES UNDER ASYMMETRIC NASH BARGAINING BETWEEN THE INSURER AND THE REINSURER

This paper examines an optimal reinsurance-investment problem involving an insurer and a reinsurer, where contractual terms are determined via an asymmetric Nash bargaining framework. Unlike conventional models assuming symmetric power, we explicitly account for heterogeneous bargaining weights, capturing the realistic imbalance in negotiating positions between the two parties. A Brownian motion with drift models the insurer’s surplus, and both the insurer and the reinsurer can invest in a financial market comprising a risk-free bond and a risky asset. The reinsurance contract and investment strategies are jointly optimized by maximizing the weighted Nash product of the parties’ expected exponential utilities of terminal wealth. We derive explicit solutions using the Hamilton-Jacobi-Bellman (HJB) equation and verify that the negotiated outcomes are Pareto optimal. Our results highlight how asymmetry in bargaining power significantly alters the optimal reinsurance and investment strategies. Numerical examples further illustrate the sensitivity of the equilibrium to model parameters, revealing novel insights into the economic implications of bargaining asymmetry in risk-sharing arrangements.