Financial Math Seminar

Abstract

This paper proposes a new framework for investigating the stochastic reinsurance game between insurer and reinsurer under model ambiguity. The insurance and reinsurance companies make decisions on the optimal reinsurance policy as a demander and a supplier of reinsurance, respectively. Meanwhile, we determine the equilibrium reinsurance price when the demand matches the supply. Both the insurer and the reinsurer aim to maximize their respective alpha-maxmin mean-variance cost functionals. We apply the second-order approximation to the entropic penalty for ambiguity and consider the variance premium principle. By solving the extended Hamilton-Jacobi-Bellman system within game theoretic framework, the equilibrium reinsurance demand-supply strategy and reinsurance price are given semi-explicitly. We find that, when the insurer and reinsurer are both ambiguity-averse, there exists a unique reinsurance price to reach the market equilibrium. While, the equilibrium price is not unique or existing for the reinsurer with ambiguity-seeking/neutral preference.