Dynamic mean-variance portfolio selection with non-shorting constraints

Xun Li, Xun Yu Zhou, Andrew E.B. Lim

Research output: Journal article publicationJournal articleAcademic researchpeer-review

208 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1540-1555
Number of pages16
JournalSIAM Journal on Control and Optimization
Issue number5
Publication statusPublished - 1 Jan 2002
Externally publishedYes


  • Continuous-time
  • Efficient frontier
  • HJB equation
  • Mean-variance portfolio selection
  • Short-selling prohibition
  • Stochastic LQ control
  • Viscosity solution

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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