Risk-Sensitive Control and an Optimal Investment Model

We consider an optimal investment model in which the goal is to maximize the long‐term growth rate of expected utility of wealth. In the model, the mean returns of the securities are explicitly affected by the underlying economic factors. The utility function is HARA. The problem is reformulated as an infinite time horizon risk‐sensitive control problem. We study the dynamic programming equation associated with this control problem and derive some consequences of the investment problem.