NDLI: Dynamic Mean-Variance Portfolio Selection with No-Shorting Constraints

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Li, Xun Lim, Andrew E. B. Zhou, Xun Yu
Copyright Year	2002
Abstract	This paper is concerned with mean-variance portfolio selection problems in continuous-time under the constraint that short-selling of stocks is prohibited. The problem is formulated as a stochastic optimal linear-quadratic (LQ) control problem. However, this LQ problem is not a conventional one in that the control (portfolio) is constrained to take nonnegative values due to the no-shorting restriction, and thereby the usual Riccati equation approach (involving a "completion of squares") does not apply directly. In addition, the corresponding Hamilton--Jacobi--Bellman (HJB) equation inherently has no smooth solution. To tackle these difficulties, a continuous function is constructed via two Riccati equations, and then it is shown that this function is a viscosity solution to the HJB equation. Solving these Riccati equations enables one to explicitly obtain the efficient frontier and efficient investment strategies for the original mean-variance problem. An example illustrating these results is also presented.
Starting Page	1540
Ending Page	1555
Page Count	16
File Format	PDF
ISSN	03630129
DOI	10.1137/S0363012900378504
e-ISSN	10957138
Issue Number	5
Volume Number	40
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-26
Access Restriction	Subscribed
Subject Keyword	short-selling prohibition viscosity solution efficient frontier HJB equation Optimal stochastic control continuous-time mean-variance portfolio selection stochastic LQ control
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics

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