  This paper deals with the general discounted impulse control problem of a
piecewise deterministic Markov process. We investigate a new family of
epsilon-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-or-intervention operator associated to the piecewise deterministic
Markov process.
