Before revision: We consider a model of optimal investment and consumption with both habit formation and partial observations in incomplete It\^{o} processes markets. The individual investor develops addictive consumption habits gradually while only observing the market stock prices but not the instantaneous rate of return , which follows an Ornstein-Uhlenbeck process . Applying the Kalman-Bucy filtering theorem and  Dynamic Programming arguments, we solve the associated HJB equation explicitly for this path dependent stochastic control problem in the case of power utility preferences .
After revision: We consider a model of optimal investment and consumption with both habit formation and partial observations in incomplete It\^{o} processes market. The investor chooses his consumption under the addictive habits constraint while only observing the market stock prices but not the instantaneous rate of return , which follows an Ornstein-Uhlenbeck process . Applying the Kalman-Bucy filtering theorem and Dynamic Programming arguments, we solve the associated HJB equation explicitly for this path dependent stochastic control problem in the case of power utility preferences .