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Numerical method for impulse control of piecewise deterministic Markov processes

Authors:	Benoîte de Saporta François Dufour

Affiliation:	1. Université de Bordeaux, GREThA CNRS UMR 5113, Avenue Léon Duguit, 33608 Pessac Cedex, France;2. Université de Bordeaux, IMB CNRS UMR 5251, 351 cours de la Libération, 33405 Talence Cedex, France;3. INRIA Bordeaux Sud Ouest team CQFD, 351 cours de la Libération, 33405 Talence Cedex, France;1. Quantitative Methods and Information Systems Area, Indian Institute of Management, Bangalore, Karnataka, 560076, India;2. Department of Mathematics, Indian Institute of Science, Karnataka, 560012, India;1. Department of Civil and Environmental Engineering, Carnegie Mellon University, United States;2. School of Computer Science, Carnegie Mellon University, United States;1. University of Twente, Enschede, Netherlands;2. Universidad Nacional de Córdoba, Córdoba, Argentina;3. Saarland University, Saarbrücken, Germany

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.

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