A long-term optimal consumption and investment problem with partial information

We consider a long-term time optimal consumption and investment problem where an investor wants to maximize the expected power utility of consumption. treat stochastic factor model that mean returns risky assets depend linearly on underlying economic factors formulated as solutions linear differential equations. also partial information case can not observe process use only past assets. Then, our is control with information. Using martingale method, we construct strategy obtain value explicitly.