Numerical method for optimal stopping of piecewise deterministic Markov processes
Benoîte de Saporta, François Dufour, and Karen Gonzalez
Source: Ann. Appl. Probab. Volume 20, Number 5
(2010), 1607-1637.
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.
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Keywords: Optimal stopping; piecewise deterministic Markov processes; quantization; numerical method; dynamic programming
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Permanent link to this document: http://projecteuclid.org/euclid.aoap/1282747395
Digital Object Identifier: doi:10.1214/09-AAP667
Zentralblatt MATH identifier: 05795065
Mathematical Reviews number (MathSciNet): MR2724397
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