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We consider a model of optimal investment and consumption with both habitformation and partial observations in incomplete It\^{o} processes market. Theinvestor chooses his consumption under the addictive habits constraint whileonly observing the market stock prices but not the instantaneous rate ofreturn. Applying the Kalman-Bucy filtering theorem and the Dynamic Programmingarguments, we solve the associated Hamilton-Jacobi-Bellman (HJB) equationexplicitly for the path dependent stochastic control problem in the case ofpower utilities. We provide the optimal investment and consumption policies inexplicit feedback forms using rigorous verification arguments.

An Explicit Example Of Optimal Portfolio-Consumption Choices With Habit Formation And Partial Observations