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Numerical method for optimal stopping of piecewise deterministic Markov processes
- Source :
- Annals of Applied Probability 2010, Vol. 20, No. 5, 1607-1637
- Publication Year :
- 2009
-
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.<br />Comment: 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)
- Subjects :
- Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Journal :
- Annals of Applied Probability 2010, Vol. 20, No. 5, 1607-1637
- Publication Type :
- Report
- Accession number :
- edsarx.0903.2114
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1214/09-AAP667