In this paper we study a general multidimensional diffusion-type stochastic
control problem. Our model contains the usual regular control problem, sin
gular control problem and impulse control problem as special cases. Using a
unified treatment of dynamic programming, we show that the value function
of the problem is a viscosity solution of certain Hamilton-Jacobi-Bellman (
HJB) quasivariational inequality. The uniqueness of such a quasi-variationa
l inequality is proved.