Time discretization and Markovian iteration for coupled FBSDES

• 成果类型: Article
• 署名作者: Bender, Christian; Zhang, Jianfeng
• 署名单位: Braunschweig University of Technology; University of Southern California
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP448
• 发表日期: 2008
• 页码: 143-177
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; regression; simulation; algorithm; options; scheme; pdes

摘要

In this paper we lay the foundation for a numerical algorithm to simulate high-dimensional coupled FBSDEs under weak coupling or monotonicity conditions. In particular, we prove convergence of a time discretization and a Markovian iteration. The iteration differs from standard Picard iterations for FBSDEs in that the dimension of the underlying Markovian process does not increase with the number of iterations. This feature seems to be indispensable for an efficient iterative scheme from a numerical point of view. We finally suggest a fully explicit numerical algorithm and present some numerical examples with up to 10-dimensional state space.