The Annals of Applied Probability

Numerical method for optimal stopping of piecewise deterministic Markov processes

Benoîte de Saporta, François Dufour, and Karen Gonzalez

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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 ε-optimal stopping time. The paper is illustrated by a numerical example.

Article information

Source
Ann. Appl. Probab., Volume 20, Number 5 (2010), 1607-1637.

Dates
First available in Project Euclid: 25 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1282747395

Digital Object Identifier
doi:10.1214/09-AAP667

Mathematical Reviews number (MathSciNet)
MR2724397

Zentralblatt MATH identifier
1197.93162

Subjects
Primary: 93E20: Optimal stochastic control
Secondary: 93E03: Stochastic systems, general 60J25: Continuous-time Markov processes on general state spaces

Keywords
Optimal stopping piecewise deterministic Markov processes quantization numerical method dynamic programming

Citation

de Saporta, Benoîte; Dufour, François; Gonzalez, Karen. Numerical method for optimal stopping of piecewise deterministic Markov processes. Ann. Appl. Probab. 20 (2010), no. 5, 1607--1637. doi:10.1214/09-AAP667. https://projecteuclid.org/euclid.aoap/1282747395


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