EconPapers    
Economics at your fingertips  
 

OPTIMAL MEAN–VARIANCE PORTFOLIO SELECTION WITH NO-SHORT-SELLING CONSTRAINT

Jingsi Xu ()
Additional contact information
Jingsi Xu: Department of Mathematics, The University of Manchester Oxford Road, Manchester, M13 9PL, UK

International Journal of Theoretical and Applied Finance (IJTAF), 2020, vol. 23, issue 08, 1-25

Abstract: In this paper, the objective is to study the continuous mean–variance portfolio selection with a no-short-selling constraint and obtain a time-consistent solution. We assume that there is a self-financing portfolio with wealth process Xtu, in which u ≥ 0 represents the fraction of wealth invested in the risk asset under the short selling prohibition. We investigate the mean–variance optimal constrained problem defined by obtaining the supremum over all admissible controls of the difference between the expectation of the value process at some designated terminal time T and a positive constant times the variance of XTu. To envisage the quadratic nonlinearity introduced by the variance, the method of Lagrangian multipliers reduces the nonlinear problem into a set of linear problems which can be solved by applying the Hamilton–Jacobi–Bellman equation and change of variables formula with local time on curves. Solving the HJB system provides the time-inconsistent solution and from there, we derive the time-consistent optimal control.

Keywords: Constrained nonlinear optimal control; static optimality; dynamic optimality; mean–variance portfolio selection; the Hamilton–Jacobi–Bellman equation; verification theorem; the change-of-variable formula with local time on curves (search for similar items in EconPapers)
Date: 2020
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219024920500545
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:23:y:2020:i:08:n:s0219024920500545

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219024920500545

Access Statistics for this article

International Journal of Theoretical and Applied Finance (IJTAF) is currently edited by L P Hughston

More articles in International Journal of Theoretical and Applied Finance (IJTAF) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().

 
Page updated 2025-03-20
Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:08:n:s0219024920500545