A numerical scheme for BSDEs

• 成果类型: Article
• 署名作者: Zhang, JF
• 署名单位: University of Southern California
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/aoap/1075828058
• 发表日期: 2004
• 页码: 459-488
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS

摘要

In this paper we propose a numerical scheme for a class of backward stochastic differential equations (BSDEs) with possible path-dependent terminal values. We prove that our scheme converges in the strong L-2 sense and derive its rate of convergence. As an intermediate step we prove an L-2-type regularity of the solution to such BSDEs. Such a notion of regularity, which can be thought of as the modulus of continuity of the paths in an L-2 sense, is new. Some other features of our scheme include the following: (i) both components of the solution are approximated by step processes (i.e., piecewise constant processes); (ii) the regularity requirements on the coefficients are practically minimum; (iii) the dimension of the integrals involved in the approximation is independent of the partition size.