Optimal investment policy for an insurer with ambiguity aversion: maximizing exponential utility of terminal wealth

Abstract

In this paper, we consider the optimal investment problem for an insurer who worries about the possibility of model misspecification. Without loss of generality, we assume there are only one risky asset and one risk-free asset in the financial market. With consideration of the existence of ambiguity, we aim to obtain the optimal investment policy with maximizing the expected utility of terminal wealth. By the dynamic optimal principle, we obtain closed-form solutions of the optimal investment policy and value function. Furthermore, we find that our study contains some results which are investigated in Browne (1995). We can see that if the insurer is ambiguity aversion, he will appear more conservative about the risky asset.