Title（问题）：On the Wellposedness of Forward-Backward SDEs—A Unified Approach

（正倒向随机微分方程可解性的统一要领）

Speaker（报告人）：Prof. Zhen Wu,山东大学

Time（时间）：2012年4月19日（周四）下昼02:00

Place（所在）：伟易博新楼217课堂

Abstract（摘要）：

The theory of Backward Stochastic Differential Equations (BSDEs) and Forward-Backward SDEs (FBSDEs) has been extensively studied for the past two decades, and its applications have been found in many branches of applied mathematics, especially the stochastic control theory and mathematical finance. The option pricing problem in the financial market and the celebrated principal-agent problem can be formulated as the forward-backward stochastic differential equations. It has been noted, however, that while in many situations the solvability of the original problems is essentially equivalent to the solvability of certain type of FBSDEs, these (mostly non-Markovian) FBSDEs are often beyond the scope of any existing frameworks.

In this talk, I will present our main result on the wellposedness of FBSDEs in a general non-Markovian framework. The main purpose is to build on all the existing methodology in the literature, and put them into a unified scheme. Our main device is a decoupling random field, and its uniform Lipschitz continuity in the spatial variable is crucial for the wellposedness of the original FBSDE. By analyzing a characteristic BSDE, which is a backward stochastic Riccati equation with quadratic growth in the Z component, we find various conditions under which such decoupling random field exists, which lead ultimately to the solvability of the original FBSDEs.

About the speaker（报告人先容）：吴臻，1971年生，山东大学数学学院教授，博士生导师，国家自然科学优异青年基金获得者，现任山东大学数学学院副院长,泰山学堂副院长。1997年于山东大学获得博士学位，法国Maine大学博士后，主要研究偏向为正倒向随机微分方程、随机最优控制及金融数学。近年来，在SIAM. J. Control Optim., IEEE Tans. Automatic Control, Automatica，J. Differential Equations等国际学术期刊揭晓SCI论文30余篇，主持认真十余项国家自然科学基金和省部级科研基金项目。曾获霍英东高校青年西席基金奖励资助，入选教育部优异青年西席资助妄想和首批教育部新世纪优异人才支持妄想，荣获山东省青年科技奖、山东省自然科学首届优异青年基金，入选山东省有突出孝顺的中青年专家。现在担当团结国教科文组织国际理论物理中心相助研究员，中国数学会理事、中国概率统计学会理事、山东省数学会副理事长和山东省人民政府金融事情办公室咨询专家。主持认真建设国家精品课程一门，两次获国家教学效果二等奖，并入选山东大学第二届“我心目中的好导师”。