Mean–variance portfolio selection with regime switching under shorting prohibition

This paper investigates a mean–variance portfolio selection problem with regime switching under the constraint of short-selling being prohibited. By applying the dynamic programming approach, a system of Hamilton–Jacobi–Bellman (HJB) equations is constructed. Recognizing the features of the optimal wealth process, the optimal feedback control and verification theorem are obtained. The efficient portfolio and efficient frontier are explicitly derived through the Lagrange multiplier approach.