Abstract
This paper concerns optimal investment problem of a CRRA investor who faces proportional transaction costs and finite time horizon. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. This enables us to make use of the well developed theory of variational inequality to study the problem. The $C^{2,1}$ regularity of the value function is proven and the optimal investment policies are completely characterized. Relying on the double obstacle problem, we extend the binomial method widely used in option pricing to determine the optimal investment policies. Numerical examples are presented as well.
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