Monte Carlo algorithms for optimal stopping and statistical learning

• 成果类型: Article
• 署名作者: Egloff, D
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000043
• 发表日期: 2005
• 页码: 1396-1432
• 关键词: american; inequalities; CONVERGENCE; approximation; bounds

摘要

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 Clement, Lamberton and Protter [Finance and Stochastics 6 (2002) 449-471].