Optimal strategies for impulse control of piecewise deterministic Markov processes
Résumé
This paper deals with the general discounted impulse control problem of a piecewise
deterministic Markov process. We investigate a new family of ǫ-optimal strategies. The
construction of such strategies is explicit and only necessitates the previous knowledge
of the cost of the no-impulse strategy. In particular, it does not require the resolution
of auxiliary optimal stopping problem or the computation of the value function at each
point of the state space. This approach is based on the iteration of a single-jump-orintervention
operator associated to the piecewise deterministic Markov process.