Numerical method for optimal stopping of piecewise deterministic Markov processes

Details Numerical method for optimal stopping of piecewise deterministic Markov processes Numerical method for optimal stopping of piecewise deterministic Markov processes

2009-03-12

arxiv.org/abs/0903.2114v2

Annals of Applied Probability 2010, Vol. 20, No. 5, 1607-1637

Mathematics

Probability

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

Scientific paper

10.1214/09-AAP667

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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