Mean-variance portfolio selection under no-shorting rules: A BSDE approach

This paper revisits the mean-variance portfolio selection problem in continuous-time within the framework of short-selling of stocks is prohibited via backward stochastic differential equation approach. To relax the strong condition in Li et al. (Li et al. 2002), the above issue is formulated as a stochastic recursive optimal linear-quadratic control problem. Due to no-shorting rules (namely, the portfolio taking non-negative values), the well-known "completion of squares" no longer applies directly. To overcome this difficulty, we study the corresponding Hamilton-Jacobi-Bellman (HJB, for short) equation inherently and derive the two groups of Riccati equations. On one hand, the value function constructed via Riccati equations is shown to be a viscosity solution of the HJB equation mentioned before; On the other hand, by means of these Riccati equations and backward semigroup, we are able to get explicitly the efficient frontier and efficient investment strategies for the recursive utility mean-variance portfolio optimization problem.(c) 2023 Elsevier B.V. All rights reserved.