Finite-horizon optimal investment with transaction costs: A parabolic double obstacle problem

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:246

Article

Dai, Min¹  Yi, Fahuai² 

[1] Natl Univ Singapore, Dept Math, Singapore 117548, Singapore

[2] S China Normal Univ, Dept Math, Guangzhou 510631, Guangdong, Peoples R China

关键词: Optimal investment;    Transaction costs;    Finite horizon;    Double obstacle problem;    Free boundary;    Singular stochastic control;    Portfolio selection;   

DOI  :  10.1016/j.jde.2008.11.003

来源: Elsevier

【 摘 要 】

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 C-2.1 regularity of the value function is proven and the behaviors of the free boundaries are completely characterized. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free