A SIMPLIFIED TREATMENT OF THE THEORY OF OPTIMAL REGULATION OF BROWNIAN-MOTION

Consider a stochastic control problem where the state variable follows a Brownian motion. The flow reward is a function of the state, which can be regulated with a lump-sum and linear cost of adjustment. Using a discrete approximation, a simple exposition of the control problem is developed. The value matching conditions that hold for any given control parameters, and the smooth pasting conditions that hold for the optimal control are derived. Some extensions and economic applications of the method are also discussed. © 1991.