Dynamic mean-variance portfolio selection with no-shorting constraints. (English) Zbl 1027.91040

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

SIAM J. Control Optimization 40, No. 5, 1540-1555 (2002).

This paper studies the mean-variance portfolio problem of choosing a self-financing strategy that minimizes the variance of final wealth for a given expected final wealth, and with the additional constraint that no short-selling is allowed in the risky assets. This problem is solved by means of stochastic linear-quadratic control methods in the context of a multidimensional Itô process model with deterministic coefficients. The authors construct a function from the solutions of two Riccati equations and show that this is a viscosity solution for the HJB equation associated to the original problem. The efficient frontier and the corresponding strategies can then be given explicitly, and an example illustrates the results.

Reviewer: Martin Schweizer (München)

MSC:

91G10	Portfolio theory
93E20	Optimal stochastic control

Keywords:

mean-variance portfolio selection; short-selling constraints; stochastic LQ control; HJB equation; viscosity solution; efficient frontier