On the optimal stochastic impulse control of linear diffusions

摘要

We consider a class of stochastic impulse control problems of linear diffusions arising in studies considering the determination of optimal dividend policies. This class of problems appears also in studies analyzing the optimal management of renewable resources. We state a set of weak conditions guaranteeing both existence and uniqueness of the boundary characterizing the optimal policy and its value. 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. In this way we extend previous findings obtained by relying on linear payoff characterizations.