Numerical method for impulse control of piecewise deterministic Markov processes

Authors:
Benoíte de Saporta;François Dufour
Affiliations:
Université de Bordeaux, GREThA CNRS UMR 5113, Avenue Léon Duguit, 33608 Pessac Cedex, France and Université de Bordeaux, IMB CNRS UMR 5251, 351 cours de la Libération, 33405 Ta ...;Université de Bordeaux, IMB CNRS UMR 5251, 351 cours de la Libération, 33405 Talence Cedex, France and INRIA Bordeaux Sud Ouest team CQFD, 351 cours de la Libération, 33405 Talence ...
Venue:
Automatica (Journal of IFAC)
Year:
2012

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Abstract

This paper presents a numerical method to calculate 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 location and inter-arrival time. Convergence results are obtained and more importantly we are able to give a convergence rate of the algorithm. The paper is illustrated by a numerical example.