Annals of Applied Probability

Monte Carlo algorithms for optimal stopping and statistical learning

Daniel Egloff

Full-text: Open access

Abstract

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].

Article information

Source
Ann. Appl. Probab., Volume 15, Number 2 (2005), 1396-1432.

Dates
First available in Project Euclid: 3 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1115137979

Digital Object Identifier
doi:10.1214/105051605000000043

Mathematical Reviews number (MathSciNet)
MR2134108

Zentralblatt MATH identifier
1125.91050

Subjects
Primary: 91B28 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 93E20: Optimal stochastic control
Secondary: 65C05: Monte Carlo methods 93E24: Least squares and related methods 62G05: Estimation

Keywords
Optimal stopping American options statistical learning empirical processes uniform law of large numbers concentration inequalities Vapnik–Chervonenkis classes Monte Carlo methods

Citation

Egloff, Daniel. Monte Carlo algorithms for optimal stopping and statistical learning. Ann. Appl. Probab. 15 (2005), no. 2, 1396--1432. doi:10.1214/105051605000000043. https://projecteuclid.org/euclid.aoap/1115137979


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