Connection between the Adjoint Variables and Value Function for

Controlled Fully Coupled FBSDEs: The Local Case

史敬涛 教授 （山东大学数学学院）

摘要：This talk is concerned with the connection between the local maximum principle and the dynamic programming principle for controlled fully coupled forward-backward stochastic differential equations (FBSDEs) when the control domain is convex and the diffusion term does not contain the variable z. The relation among the adjoint variables and the value function is obtained within the viscosity solution framework. The first-order adjoint equation of [M.S. Hu, S.L. Ji and X.L. Xue, A global stochastic maximum principle for fully coupled forward-backward stochastic systems,arXiv: 1803.02109] can be derived from the adjoint FBSDE of [Z. Wu, Maximum principle for optimal control problem of fully coupled forward-backward stochastic systems, Systems Science and Mathematical Sciences, vol. 11, 1998, pp. 249-259], by our main theorem. Additionally, we give an example to show the applications of the theoretical result. This talk is based on a joint work with my PhD candidate, Weijun Meng（孟维君）。

报告人简介： 史敬涛，男， 1978 年生，山东大学数学学院教授、博士生导师，概率统计研究所党支部书记。 2003 年参加工作， 2009 年获理学博士学位。主要从事随机控制、微分对策、正倒向随机系统、时滞随机系统与金融数学等领域的研究。曾赴美国、英国、瑞典、日本、澳大利亚、新加坡、台湾、香港、澳门等国家和地区学术访问交流。在 IEEE Transactions on Automatic Control、Automatica,、 SIAM Journal on Control and Optimization 等国际重要学术期刊和IEEE International Conference on Control and Automation、 American Control Conference、 IFAC Symposium on Nonlinear Control System 等国际重要学术会议发表学术论文 50 余篇。曾获中国科协期刊优秀学术论文奖、张嗣瀛优秀青年论文奖、山东省高校优秀科研成果奖等奖项，主持多项国家和山东省自然科学基金项目，参与国家自然科学基金重点项目。现为中国自动化学会控制论专业委员会随机系统控制学组委员。目前指导博士研究生 1 名，硕士研究生十余名。