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. We treat a stochastic factor model that the mean returns of risky assets depend linearly on underlying economic factors formulated as the solutions of linear stochastic differential equations. We also treat the partial information case that the investor can not observe the factor process and use only past information of risky assets. Then, our problem is formulated as a stochastic control problem with partial information. Using the martingale method, we construct the optimal strategy and obtain the optimal value explicitly.