| Abstract: |
| We consider optimal consumption problem on finite time or on infinite time horizon. An investor wants
to maximize the expected HARA utility of consumption . We treat a stochastic factor model that the mean returns of risky assets depend linearly on underlying economic factors formulated as the solutions of linear stochastic differential equations. We discuss the partial information case that the investor can not observe the factor process and use only past information of risky assets. Then our problem is formulated as a stochastic control problem with partial information. Using filtering equation, we can reformulate the problem with complete information. We derive the HJB equation. The equation can be solved to obtain an explicit form of the value function and the optimal strategy for this problem. Moreover, we also introduce martingale method and obtain solution without solving PDE. We compare the solution using dynamic programming approach and martingale method.
The discussion is based on a joint work with Hiroaki Hata. |
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