Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jde.2008.11.003
Title: Finite-horizon optimal investment with transaction costs: A parabolic double obstacle problem
Authors: Dai, M. 
Yi, F.
Keywords: Double obstacle problem
Finite horizon
Free boundary
Optimal investment
Portfolio selection
Singular stochastic control
Transaction costs
Issue Date: 15-Feb-2009
Citation: Dai, M., Yi, F. (2009-02-15). Finite-horizon optimal investment with transaction costs: A parabolic double obstacle problem. Journal of Differential Equations 246 (4) : 1445-1469. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jde.2008.11.003
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. © 2008 Elsevier Inc. All rights reserved.
Source Title: Journal of Differential Equations
URI: http://scholarbank.nus.edu.sg/handle/10635/103274
ISSN: 00220396
DOI: 10.1016/j.jde.2008.11.003
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