Before revision:  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:  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 the Dynamic Programming arguments, we solve the associated HJB equation explicitly for this path dependent stochastic control problem in the case of power utility preferences .