金融工程研究中心学术报告：Mean Field Games, their FBSDEs and Master Equations

报 告 人： Sheung Chi Phillip Yam  The Chinese University of Hong Kong 报告时间： 2023年10月24日星期二  16:30-17:15 报告地点：览秀楼105学术报告厅 报告摘要： Modeling collective behaviors of individuals in account of their mutual interactions arisen in various physical or sociological dynamical systems have been one of the major problems in the history of mankind. To resolve this matter, a completely different macroscopic approach inspired from statistical physics had been gradually developed in the last decade, which eventually leads to the primitive notion of mean field game theory. In this talk, we shall introduce a theory of global-in-time well-posedness for a general class of mean field game problems, which include as an example settings with quasi-convex payoff functions as long as the mean field sensitivity is not too large. Through the stochastic maximum principle, we adopt the forward backward stochastic differential equation (FBSDE) approach to investigate the unique existence of the corresponding equilibrium strategies. This FBSDE is first solved locally in time, then by controlling the sensitivity with respect to the initial condition of the solution to the backward equation via studying its Jacobian flow, the global-in-time solution is warranted. Further analysis of the Jacobian flow of the solution to the FBSDE will be discussed so as to establish the regularities of the value function, including its linear functional differentiability, that also leads to the classical well-posedness of the complicated one-directional master equations on R^n. In contrast to the recent approach with an emphasis on the well-posedness of the master equations, we solve the whole problem by tackling the mean field game equilibrium problems directly; indeed, we extend the well-posedness result in [P. Caradaliaguet, F. Delarue, J.-M. Lasry, and P.-L. Lions. The master equation and the convergence problem in mean field games:(ams-201).], which founds their theory on a torus in a Holder space, to the whole unbounded domain R^n via the Sobolev space language.   个人简介： Phillip Yam received his BSc in Actuarial Science with first class honours and MPhil from the University of Hong Kong. Supported by the two scholarships awarded by the Croucher Foundation (Hong Kong), he obtained an MASt (Master of Advanced Study) degree, Part III of the Mathematical Tripos, with Distinction in Mathematics from University of Cambridge and a DPhil in Mathematics from University of Oxford. During his postgraduate studies, he was awarded with the E. M. Burnett Prize in Mathematics from University of Cambridge, and the junior research fellowship from The Erwin Schr?dinger International Institute for Mathematics and Physics of University of Vienna. Phillip is currently the Co-Director of the Interdisciplinary Major Program in Quantitative Finance and Risk Management Science, and a full Professor at the Department of Statistics of CUHK. He is also Assistant Dean (Education) of CUHK Faculty of Science, and Fellow of the Centre for Promoting Science Education in the Faculty. He got appointed as a research fellow in the Hausdorff Research Institute for Mathematics of University of Bonn and a Visiting Professor in the Department of Statistics of Columbia University in the City of New York. He has about a hundred journal articles in actuarial science and financial mathematics, applied mathematics, engineering, and statistics, and has also been serving in editorial boards of several journals in these fields. Together with Alain Bensoussan and Jens Frehse, he wrote up the first monograph on mean field games and mean field type control theory. His research project with the title "Comonotone-independence Bayes Classifier (CIBer)" was awarded a Silver Medal in the 48th International Exhibition of Inventions Geneva in 2023.