REGRESSION ANYTIME WITH BRUTE-FORCE SVD TRUNCATION

• 成果类型: Article
• 署名作者: Bender, Christian; Schweizer, Nikolaus
• 署名单位: Saarland University; Tilburg University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1615
• 发表日期: 2021
• 页码: 1140-1179
• 关键词: simulation; approximation; CONVERGENCE; algorithm; portfolio; options; scheme; bounds

摘要

We propose a new least-squares Monte Carlo algorithm for the approximation of conditional expectations in the presence of stochastic derivative weights. The algorithm can serve as a building block for solving dynamic programming equations, which arise, for example, in nonlinear option pricing problems or in probabilistic discretization schemes for fully nonlinear parabolic partial differential equations. Our algorithm can be generically applied when the underlying dynamics stem from an Euler approximation to a stochastic differential equation. A built-in variance reduction ensures that the convergence in the number of samples to the true regression function takes place at an arbitrarily fast polynomial rate, if the problem under consideration is smooth enough.