A Direct Solution Method for Stochastic Impulse Control Problems of One-dimensional Diffusions

Abstract

We consider stochastic impulse control problems where the process is driven by a general one-dimensional diffusion. We shall show a new mathematical characterization of the value function as a linear function in a certain transformed space. Our approach can relieve us from the burden of guessing and proving the optimal strategy, (2) present a simple method to find the value function and the corresponding control policies, and (3) handle systematically a broader class of reward and cost functions since the existence of the value function can be shown in much a simpler way.