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Optimal Mean–Variance Portfolio Selection With No-Short-Selling Constraint

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  • JINGSI XU

    (Department of Mathematics, The University of Manchester Oxford Road, Manchester, M13 9PL, UK)

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.

Suggested Citation

  • Jingsi Xu, 2020. "Optimal Mean–Variance Portfolio Selection With No-Short-Selling Constraint," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(08), pages 1-25, December.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:08:n:s0219024920500545
    DOI: 10.1142/S0219024920500545
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