DE SAPORTA, Benoîte; DUFOUR, François; GONZALEZ, Karen

doi:10.1214/09-AAP667

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DE SAPORTA, Benoîte
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Groupe de Recherche en Economie Théorique et Appliquée [GREThA]

DUFOUR, François
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]

GONZALEZ, Karen
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]

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Ce document a été publié dans

The Annals of Applied Probability. 2010, vol. 20, n° 5, p. 1607-1637

Institute of Mathematical Statistics (IMS)

Résumé en anglais

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.< Réduire