SIMULATION OF BSDES BY WIENER CHAOS EXPANSION

• 成果类型: Article
• 署名作者: Briand, Philippe; Labart, Celine
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Universite Savoie Mont Blanc; CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP943
• 发表日期: 2014
• 页码: 1129-1171
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; Discretization; algorithm; scheme

摘要

We present an algorithm to solve BSDEs based on Wiener chaos expansion and Picard's iterations. We get a forward scheme where the conditional expectations are easily computed thanks to chaos decomposition formulas. We use the Malliavin derivative to compute Z. Concerning the error, we derive explicit bounds with respect to the number of chaos and the discretization time step. We also present numerical experiments. We obtain very encouraging results in terms of speed and accuracy.