MALLIAVIN CALCULUS FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS AND APPLICATION TO NUMERICAL SOLUTIONS

• 成果类型: Article
• 署名作者: Hu, Yaozhong; Nualart, David; Song, Xiaoming
• 署名单位: University of Kansas
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP762
• 发表日期: 2011
• 页码: 2379-2423
• 关键词: path regularity; scheme

摘要

In this paper we study backward stochastic differential equations with general terminal value and general random generator. In particular, we do not require the terminal value be given by a forward diffusion equation. The randomness of the generator does not need to be from a forward equation, either. Motivated from applications to numerical simulations, first we obtain the L(p)-Holder continuity of the solution. Then we construct several numerical approximation schemes for backward stochastic differential equations and obtain the rate of convergence of the schemes based on the obtained L(p)-Holder continuity results. The main tool is the Malliavin calculus.