In the paper risk sensitive portfolio optimization model introduced by Bielecki and Pliska is studied. It is assumed that the price of assets depends on economical factors. Some factors are completely and the other only partially observed. We want to maximize risk sensitized growth rate of the capital process.
The problem is to find a solution to a suitable Bellman equation which corresponds to the problem. For this purpose discounted risk sensitized problem is considered. Letting discount factor go to 1, we show that suitably normalized value function of the discounted control problem approaches a solution to the Bellman equation of the original problem.
The optimal strategies of risk sensitive control problem depend on the current observation of the observable factors and a normalization of the measure valued process which provides an information about the unobserved factors.