ABSTRACT

The first part of the talk will be devoted to a review of the theory of mean field games and mean field control, with a special emphasis on the probabilistic approach. Next, we shall discuss several new research agendas including graphon games and mean field reinforcement learning.  Finally, we shall present recent results on: 1) the use of machine learning techniques to numerically compute equilibria; 2) the analysis of finite state space models and their applications to the control of the spread of diseases; 3) mean field Q- learning.

BIOGRAPHY

René Carmona, Ph.D., is the Paul M. Wythes ’55 Professor of Engineering and Finance at Princeton University in the department of Operations Research and Financial Engineering. He is an associate member of the Department of Mathematics, a member of the Program in Applied and Computational Mathematics, and Director of Graduate Studies of the Bendheim Center for Finance where he oversees the Master in Finance program. He obtained a PhD in probability from Marseille university where he held his first academic job. After time spent at Cornell and a couple of stints at Princeton, he moved to the University of California at Irvine in 1981 and eventually Princeton University in 1995.

Dr. Carmona is a Fellow of the Institute of Mathematical Statistics, the Society for Industrial and Applied Mathematics and the American Mathematical Society. He is the founding chair of the SIAM Activity Group on Financial Mathematics and Engineering, a founding editor of the Electronic Journal & Communications in Probability, and the SIAM Journal on Financial Mathematics. He is on the editorial board of several peer-reviewed journals and book series. He organized conferences and summer schools on Energy Risk,  the Future of the Electricity Markets, Emissions Regulations, and high frequency trading, topics on which he designed and taught courses and tutorials.

His publications include over one hundred articles and eleven books in probability, statistics, mathematical physics, signal analysis and financial mathematics. He also developed computer programs for teaching and research. He has worked on the commodity and energy markets as well as the credit markets, and he is recognized as a leading researcher and consultant in these areas. Over the last decade his research focused on the development of a probabilistic approach to Mean Field Games and Mean Field Control. In collaboration with F. Delarue, he wrote a two volume book providing the state of the art on the subject. In January 2020, this book was the recipient of the J.L. Doob Prize, awarded every three years by the American Mathematical Society.