Equilibrium reinsurance price under α -maxmin mean-variance criterion: a view of demand and supply

In this paper, we develop an innovative framework for reinsurance contracting problem under model ambiguity. The insurer and the reinsurer take the roles of demander and supplier in reinsurance market, respectively. Both parties aim to maximize their respective alpha α α -maxmin mean-variance performance functional. They choose optimal reinsurance policies, and the equilibrium reinsurance price is determined by clearing the market for demand and supply. The reinsurance premium is calculated according to the variance premium principle. For tractability, we apply the second-order approximation to the entropic penalty for ambiguity. By solving the extended Hamilton–Jacobi–Bellman equation system within the game-theoretic framework, the semi-explicit expressions for the equilibrium reinsurance demand-supply strategy and the reinsurance price have been derived. A key finding is that when both players are ambiguity-averse, a unique equilibrium reinsurance price always exists; by contrast, with ambiguity-seeking/neutral preferences, a market equilibrium reinsurance price may fail to exist.