Finite-horizon optimal investment with transaction costs: A parabolic double obstacle problem |
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Authors: | Min Dai Fahuai Yi |
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Institution: | a Dept. of Math., National University of Singapore, Singapore b Dept. of Math., South China Normal University, Guangzhou 510631, China |
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Abstract: | This paper concerns optimal investment problem of a CRRA investor who faces proportional transaction costs and finite time horizon. From the angle of stochastic control, it is a singular control problem, whose value function is governed by a time-dependent HJB equation with gradient constraints. 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 obstacle problem to attack the problem. The C2,1 regularity of the value function is proven and the behaviors of the free boundaries are completely characterized. |
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Keywords: | Optimal investment Transaction costs Finite horizon Double obstacle problem Free boundary Singular stochastic control Portfolio selection |
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