SECOND ORDER DISCRETIZATION OF BACKWARD SDES AND SIMULATION WITH THE CUBATURE METHOD

• 成果类型: Article
• 署名作者: Crisan, Dan; Manolarakis, Konstantinos
• 署名单位: Imperial College London
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP932
• 发表日期: 2014
• 页码: 652-678
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; quantization algorithm; scheme

摘要

We propose a second order discretization for backward stochastic differential equations (BSDEs) with possibly nonsmooth boundary data. When implemented, the discretization method requires essentially the same computational effort with the Euler scheme for BSDEs of Bouchard and Touzi [Stochastic Process. Appl. 111 (2004) 175-206] and Zhang [Ann. AppL Probab. 14 (2004) 459-488]. However, it enjoys a second order asymptotic rate of convergence, provided that the coefficients of the equation are sufficiently smooth. In the second part of the paper, we combine this discretization with higher order cubature formulas on Wiener space to produce a fully implementable second order scheme.