Approximation of the value function of an impulse control problem of Piecewise Deterministic Markov Processes
Résumé
This paper presents a numerical method to approximate the value function for a general discounted impulse control problem for piecewise deterministic Markov processes. Our approach is based on a quantization technique for the underlying Markov chain defined by the post jump locations and inter-arrival times. Convergence results are obtained and more importantly we are able to give a convergence rate of the algorithm. This paper is illustrated by an example.