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.

Published in at http://dx.doi.org/10.1214/09-AAP667 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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