Numerical method for impulse control of Piecewise Deterministic Markov Processes

Details Numerical method for impulse control of Piecewise Deterministic Markov Processes Numerical method for impulse control of Piecewise Deterministic Markov Processes

2010-11-26

arxiv.org/abs/1011.5812v2

Mathematics

Probability

This work was supported by ARPEGE program of the French National Agency of Research (ANR), project "FAUTOCOES", number ANR-09-

Scientific paper

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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