Equilibrium investment and reinsurance strategies under smooth ambiguity with a general second-order distribution

Abstract

This paper studies an optimal investment and reinsurance problem under the smooth ambiguity model proposed by Klibanoff et al. (2005). We assume the mean-variance criterion for risk preferences and constant absolute ambiguity aversion for ambiguity preferences. In light of time inconsistency, closed-form equilibrium investment and reinsurance strategies are obtained for a general second-order distribution for financial and insurance risks. This generality provides great flexibility for decision makers to model ambiguity and assigns a diverse array of weights to the set of prior probability measures. To tackle the challenge from a general second-order distribution, we investigate the impact of ambiguity attitudes on the equilibrium strategies analytically by adopting the comparison principle method for the associated differential equations. We find smooth ambiguity can generate richer forms of optimal strategies than other ambiguity models, which highlights the importance and distinction of smooth ambiguity.