An Optimal Portfolio Problem for An Insurer with Consumer Price Index and Partial Information

We consider an optimal portfolio problem with consumer price index (CPI) and partial information in a continuous time setting, where the insurer attempts to maximize her expected constant absolute risk aversion (CARA) utility of terminal wealth. In our model, both the partially observed stochastic factor process of the stock market and the fully observed surplus process of the insurance market are considered. By Kalman-Bucy filter, the stochastic optimal control problem with partial information is transformed into the stochastic optimal control problem with complete information. And then in order to obtain the explicit solution of the optimal strategy in CARA class, we solve the Hamilton-Jacobi-Bellman (HJB) equation and prove its verification theorem.