ON WELL-POSEDNESS OF FORWARD-BACKWARD SDES-A UNIFIED APPROACH

• 成果类型: Article
• 署名作者: Ma, Jin; Wu, Zhen; Zhang, Detao; Zhang, Jianfeng
• 署名单位: University of Southern California; Shandong University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1046
• 发表日期: 2015
• 页码: 2168-2214
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; random-coefficients; riccati-equations; quadratic growth; adapted solution; fbsdes; pdes

摘要

In this paper, we study the well-posedness of the Forward Backward Stochastic Differential Equations (FBSDE) in a general non-Markovian framework. The main purpose is to find a unified scheme which combines all existing methodology in the literature, and to address some fundamental long-standing problems for non-Markovian FBSDEs. An important device is a decoupling random field that is regular (uniformly Lipschitz in its spatial variable). We show that the regulariy of such decoupling field is closely related to the bounded solution to an associated characteristic BSDE, a backward stochastic Riccati-type equation with superlinear growth in both components Y and Z. We establish various sufficient conditions for the well-posedness of an ODE that dominates the characteristic BSDE, which leads to the existence of the desired regular decoupling random field, whence the solvability of the original FBSDE. A synthetic analysis of the solvability is given, as a User's Guide, for a large class of FBSDEs that are not covered by the existing methods. Some of them have important implications in applications.