  This paper concerns a continuous time mean-variance (MV) portfolio selection
problem in a jump-diffusion financial model with no-shorting trading
constraint. The problem is reduced to two subproblems: solving a stochastic
linear-quadratic (LQ) control problem under control constraint, and finding a
maximal point of a real function. Based on a two-dimensional fully coupled
ordinary differential equation (ODE), we construct an explicit viscosity
solution to the Hamilton-Jacobi-Bellman equation of the constrained LQ problem.
Together with the Meyer-It\^o formula and a verification procedure, we obtain
the optimal feedback controls of the constrained LQ problem and the original MV
problem, which corrects the flawed results in some existing literatures. In
addition, closed-form efficient portfolio and efficient frontier are derived.
In the end, we present several examples where the two-dimensional ODE is
decoupled.
