  In this paper, we study a free boundary problem, which arises from an optimal
trading problem of a stock that is driven by a uncertain market status process.
The free boundary problem is a variational inequality system of three functions
with a degenerate operator. The main contribution of this paper is that we not
only prove all the four switching free boundaries are no-overlapping, monotonic
and $C^{\infty}$-smooth, but also completely determine their relative
localities and provide the optimal trading strategies for the stock trading
problem.
