We consider a model of optimal investment and consumption with both habit-formation and partial observations in incomplete Ito processes markets. 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. We will 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 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.
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habit-formation
habit formation
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Ito
It\^{o
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he can only observe
only observing
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rates
rate
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follow
follows an
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processes
process
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fully
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will