Open Access
May 2005 Monte Carlo algorithms for optimal stopping and statistical learning
Daniel Egloff
Ann. Appl. Probab. 15(2): 1396-1432 (May 2005). DOI: 10.1214/105051605000000043


We extend the Longstaff–Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical learning problem. Within this setup we apply deviation inequalities for suprema of empirical processes to derive consistency criteria, and to estimate the convergence rate and sample complexity. Our results strengthen and extend earlier results obtained by Clément, Lamberton and Protter [Finance and Stochastics 6 (2002) 449–471].


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Daniel Egloff. "Monte Carlo algorithms for optimal stopping and statistical learning." Ann. Appl. Probab. 15 (2) 1396 - 1432, May 2005.


Published: May 2005
First available in Project Euclid: 3 May 2005

zbMATH: 1125.91050
MathSciNet: MR2134108
Digital Object Identifier: 10.1214/105051605000000043

Primary: 60G40 , 91B28 , 93E20
Secondary: 62G05 , 65C05 , 93E24

Keywords: American options , Concentration inequalities , Empirical processes , Monte Carlo methods , Optimal stopping , Statistical learning , uniform law of large numbers , Vapnik–Chervonenkis classes

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.15 • No. 2 • May 2005
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