Abstract
This paper deals with the general discounted impulse control problem of a piecewisedeterministic Markov process. We investigate a new family of ǫ-optimal strategies. Theconstruction of such strategies is explicit and only necessitates the previous knowledgeof the cost of the no-impulse strategy. In particular, it does not require the resolutionof auxiliary optimal stopping problem or the computation of the value function at eachpoint of the state space. This approach is based on the iteration of a single-jump-orinterventionoperator associated to the piecewise deterministic Markov process.