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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.
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