SIAM Journal on Control and Optimization, Vol.38, No.5, 1603-1622, 2000
Optimal policies for n-dimensional singular stochastic control problems part I: The Skorokhod problem
An n-dimensional Brownian motion is controlled by adding a process of locally bounded variation to it so as to minimize an expected infinite-horizon discounted cost. We show, by direct probabilistic techniques, that the optimal control is a solution of a ( generalized) Skorokhod problem.