主讲人:山东大学数学学院 吴臻教授
题 目：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方法）
主持人：西南财经大学经济数学学院 向开理教授
地 点: 西南财经大学柳林校区E201教室
时 间：2013年7月2日（星期二）下午4:30-6:00
主 办：经济数学学院 科研处
报告摘要:
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 inthe 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.
报告人简介:
吴臻，山东大学数学学院党委书记、副院长，教授，博士生导师，教育部 “****”首批特聘教授彭实戈院士创新学术团队骨干成员之一,国家重点学科山东大学运筹学与控制论专业青年学术带头人。入选2002 年度教育部优秀青年教师资助计划和2004 年度教育部首批新世纪优秀人才支持计划，2004 年获霍英东高校青年教师基金奖励资助，2005 年被评为山东省优秀青年知识分子，2008年获第八届山东省青年科技奖，2008 年获山东省首届杰出青年基金（数学学科唯一入选者），2009 年入选山东省有突出贡献的中青年专家,2011年获国家杰出青年基金资助。
吴臻教授的研究领域涉及随机控制、概率论和金融数学等方面，主要研究方向为正倒向随机微分方程与随机最优控制理论，既是重要的理论课题，又在金融数学方面有很强的应用背景。与国际知名随机控制专家J. P. Lepeltier 教授、S. Hamadene 教授，金融学家M. Bellalah 教授及彭实戈院士合作，取得了较突出的科研成绩。近五年来，吴臻教授在SIAM. J. Control Optim., IEEE Trans. Autom. Control, Automatica，J. Diff. Equa., Ann. Oper.
