On the Optimal Stochastic Impulse Control of Linear Diffusions

We consider a class of stochastic impulse control problems of linear diffusions arising in studies considering the determination of optimal dividend policies and in studies analyzing the optimal management of renewable resources. We derive a set of weak conditions guaranteeing both the existence and uniqueness of the optimal policy and its value by relying on a combination of the classical theory of diffusions, stochastic calculus, and ordinary nonlinear programming techniques. We also analyze two associated stochastic control problems and establish a general ordering for both the values and the marginal values of the considered stochastic control problems. CONTENTS