Ma, Jin et Yong, Jiongmin, Dynamic programming for multidimensional stochastic control problems, Acta mathematica Sinica. English series (Print) , 15(4), 1999, pp. 484-506
In this paper we study a general multidimensional diffusion-type stochastic control problem. Our model contains the usual regular control problem, singular 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-variational inequality is proved.