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Symposium on Probability and Analysis 2010 Institute of Mathematics, Academia Sinica, Taipei, Taiwan An optimal consumption problem with partial information Hiroaki Hata August 10 - 12, 2010 Institute of Mathematics, Academia Sinica Taipei, 10617 Taiwan E-mail:[email protected] Abstract We consider an optimal consumption problem where an investor tries to maximize the finite horizon expected discounted HARA utility of consumption. We treat a stochastic factor model that the mean returns of risky assets depend on underlying economic factors formulated as the solution of a linear stochastic differential equation. We also discuss the partial information case that an investor use only past information of risky assets without using factor processes. Then our problem is formulated as a kind of stochastic control problem with partial information. As a result, we obtain explicit forms of the value function and the optimal strategy for this problem. 1