Approximation of the value function of an impulse control problem of Piecewise Deterministic Markov Processes

Benoîte de Saporta (1, 2, 3) , François Dufour (2, 3) , Huilong Zhang (2, 3)

1 GREThA - Groupe de Recherche en Economie Théorique et Appliquée
2 IMB - Institut de Mathématiques de Bordeaux
3 CQFD - Quality control and dynamic reliability

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.

Mots clés: hybrid processes; piecewise deterministic Markov processes; quantization; convergence of numerical method; dynamic programming; numeric control

Domaines: Probabilités [math.PR]

Benoîte de Saporta, François Dufour, Huilong Zhang. Approximation of the value function of an impulse control problem of Piecewise Deterministic Markov Processes. 18th IFAC world congress, 2011, Milano, Italy. pp.TuA09.2. ⟨hal-00617822⟩