Before revision:  The individual investor develops addictive consumption habits gradually while he can only observe the market stock prices but not the instantaneous rates of return, which follow Ornstein-Uhlenbeck processes . Applying the Kalman-Bucy filtering theorem and Dynamic Programming arguments, we solve the associated HJB equation fully 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 he can only observe the market stock prices but not the instantaneous rates of return, which follow Ornstein-Uhlenbeck process . Applying the Kalman-Bucy filtering theorem and Dynamic Programming arguments, we solve the associated HJB equation fully explicitly for this path dependent stochastic control problem in the case of power utility preferences.