Optimal investment and risk control policies for an insurer: Expected utility maximization

Motivated by the AIG bailout case in the financial crisis of 2007-2008, we consider an insurer who wants to maximize his/her expected utility of terminal wealth by selecting optimal investment and risk control strategies. The insurer's risk process is modeled by a jump-diffusion process and is negatively correlated with the capital gains in the financial market. We obtain explicit solutions of optimal strategies for various utility functions.