  This paper concerns the continuous time mean-variance portfolio selection
problem with a special nonlinear wealth equation. This nonlinear wealth
equation has a nonsmooth coefficient and the dual method developed in [6] does
not work. We invoke the HJB equation of this problem and give an explicit
viscosity solution of the HJB equation. Furthermore, via this explicit
viscosity solution, we obtain explicitly the efficient portfolio strategy and
efficient frontier for this problem. Finally, we show that our nonlinear wealth
equation can cover three important cases.
