A Class of Solvable Stationary Singular Stochastic Control Problems

We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic control theory. We present a set of conditions under which the optimal policy is of the standard local time reflection type and state the first order conditions from which the boundaries can be determined. Since the conditions do not require symmetry or convexity of the costs, our results cover also the cases where costs are asymmetric and non-convex. We also investigate the comparative static properties of the optimal policy and delineate circumstances under which higher volatility expands the continuation region where utilizing the control is suboptimal.