A solution technique for Lévy driven long term average impulse control problems

Abstract

This article treats long term average impulse control problems with running costs in the case that the underlying process is a Lévy process. Assuming a maximum representation for the payoff function, we give easy to verify conditions for the control problem to have an s,S strategy as an optimizer. The occurring thresholds are given by the roots of an explicit auxiliary function. This leads to a step by step solution technique whose utility we demonstrate by solving a variety of examples of impulse control problems.