Abstract: In this talk, we study the wellposedness 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 overcome some fundamental difficulties that have been longstanding problems for non-Markovian FBSDEs. Our main devices are a decoupling random field and its associated characteristic BSDE, a backward stochastic Riccati-type equation with superlinear growth in both components Y and Z. We establish various sufficient conditions under which the characteristic BSDE is wellposed, which leads to the existence of the decoupling random field, and ultimately to the solvability of the original FBSDE. A synthetic analysis for solvability conditions will be 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.

 

张德涛博士简历：1981年6月生，山东大学经济学院，讲师，先后于2004年、2007年、2010年在山东大学数学学院获学士、硕士、博士学位。2009年-2010年，受国家留学基金委的资助，赴美国南加州大学(USC)数学系交流访问，师从国际著名的随机控制、金融数学专家Jin Ma教授和Jianfeng Zhang教授。目前主要从事金融数学，随机控制、正倒向随机微分方程等方面的研究。目前主持1项山东大学自主创新基金，主要参与多项国家自然科学基金项目。完成发表论文6篇，其中SCI论文2篇，EI论文2篇。