Numerical method for optimal stopping of piecewise deterministic Markov processes

Abstract : We propose a numerical method to approximate the value function for the optimal stopping problem of a piecewise deterministic Markov process (PDMP). Our approach is based on quantization of the post jump location -- inter-arrival time Markov chain naturally embedded in the PDMP, and path-adapted time discretization grids. It allows us to derive bounds for the convergence rate of the algorithm and to provide a computable epsilon-optimal stopping time. The paper is illustrated by a numerical example.
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https://hal.archives-ouvertes.fr/hal-00367964
Contributor : Benoîte De Saporta <>
Submitted on : Friday, March 13, 2009 - 9:45:40 AM
Last modification on : Monday, February 18, 2019 - 7:52:10 PM

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  • HAL Id : hal-00367964, version 1
  • ARXIV : 0903.2114

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Benoîte De Saporta, François Dufour, Karen Gonzalez. Numerical method for optimal stopping of piecewise deterministic Markov processes. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2010, 20 (5), pp.1607-1637. 〈hal-00367964〉

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