OPTIMAL INVESTMENT STRATEGY FOR AN INSURER WITH PARTIAL INFORMATION IN CAPITAL AND INSURANCE MARKETS

This paper considers a framework in which an insurer determines the optimal investment strategies to maximize the expected utility of terminal wealth. We obtain the optimal investment strategies assuming that both the capital market and the insurance market are partially observable. By employing Bayesian method and filtering theory, we first transform the optimization problem with partial information into the one with complete information. We then achieve the explicit expression of the optimal investment strategy by using dynamic programming principle. In addition, we also derive the optimal investment strategies with complete information in both markets as well as partial information in either market. Finally, we compare the optimal strategies in different models and study value functions numerically to illustrate our results.