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On the forward algorithm for stopping problems on continuous-time Markov chains

Part of: Markov processes Mathematical finance

Published online by Cambridge University Press:  22 November 2021

Laurent Miclo  and
Stéphane Villeneuve
Laurent Miclo*
Affiliation:
CNRS and Université de Toulouse
Stéphane Villeneuve*
Affiliation:
Université de Toulouse
*
*Postal address: Toulouse School of Economics, 1 Esplanade de l’université, 31080 Toulouse cedex 06, France.
*Postal address: Toulouse School of Economics, 1 Esplanade de l’université, 31080 Toulouse cedex 06, France.
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Abstract

We revisit the forward algorithm, developed by Irle, to characterize both the value function and the stopping set for a large class of optimal stopping problems on continuous-time Markov chains. Our objective is to renew interest in this constructive method by showing its usefulness in solving some constrained optimal stopping problems that have emerged recently.

Keywords

Forward algorithmconstrained optimal stoppingMarkov chains

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J45: Probabilistic potential theory 60J28: Applications of continuous-time Markov processes on discrete state spaces 90C40: Markov and semi-Markov decision processes 91G60: Numerical methods (including Monte Carlo methods)
Type
Original Article
Information
Journal of Applied Probability , Volume 58 , Issue 4 , December 2021 , pp. 1043 - 1063
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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