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 . We provide the optimal investment and consumption policies in explicit feedback forms using rigorous verification arguments.
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 . Applying the Kalman-Bucy filtering theorem and the Dynamic Programming arguments, we solve the associated Hamilton-Jacobi-Bellman (HJB) equation explicitly for the path dependent stochastic control problem in the case of power utilities . We provide the optimal investment and consumption policies in explicit feedback forms using rigorous verification arguments.
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markets. The individual investor develops addictive consumption habits gradually
market. The investor chooses his consumption under the addictive habits constraint
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, which follows an Ornstein-Uhlenbeck process
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the
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HJB
Hamilton-Jacobi-Bellman (HJB)
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this
the
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utility preferences
utilities