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 ε-optimal stopping time. The paper is illustrated by a numerical example.
@article{1282747395,
author = {de Saporta, Beno\^\i te and Dufour, Fran\c cois and Gonzalez, Karen},
title = {Numerical method for optimal stopping of piecewise deterministic Markov processes},
journal = {Ann. Appl. Probab.},
volume = {20},
number = {1},
year = {2010},
pages = { 1607-1637},
language = {en},
url = {http://dml.mathdoc.fr/item/1282747395}
}
de Saporta, Benoîte; Dufour, François; Gonzalez, Karen. Numerical method for optimal stopping of piecewise deterministic Markov processes. Ann. Appl. Probab., Tome 20 (2010) no. 1, pp. 1607-1637. http://gdmltest.u-ga.fr/item/1282747395/