Columbia-NYU Financial Engineering Colloquium: Erhan Bayraktar & Mathieu Lauriere

Erhan Bayraktar, University of Michigan

Title

Prediction problems and second order parabolic equations in the Wasserstein space

Abstract

We study the long-time regime of the prediction with expert advice problems in both full information and adversarial bandit feedback settings. In the adversarial bandit feedback setting, we show that the problem leads to second order parabolic PDEs in the Wasserstein space. We establish the wellposedness of weak solutions for these PDEs and establish the connection between these PDEs, mean-field control, and filtering problems. Based on joint works with Ibrahim Ekren and Xin Zhang.

Bio

Erhan Bayraktar, the holder of the Susan Smith Chair, is a full professor of Mathematics at the University of Michigan, where he has been since 2004. Professor Bayraktar's research is in stochastic analysis, control, applied probability, mean field games, machine learning, and mathematical finance.  He is a corresponding editor in the SIAM Journal on Control and Optimization and also serves on the editorial boards of Applied Mathematics and Optimization, Frontiers in Mathematical Finance, Mathematics of Operations Research, and Mathematical Finance. His research has also been continually funded by the National Science Foundation. In particular, he received a CAREER grant.  Professor Bayraktar has been the director of the Risk Management and Quantitative Finance Masters program since its inception in 2015. He has had 14 Ph.D. students and over 40 post-docs. 

Mathieu Laurière, NYU Shanghai

Title

Deep Learning for Stackelberg Mean Field Games via Single-Level Reformulation

Abstract

We propose a single-level numerical approach to solve Stackelberg mean field game (MFG) problems. In Stackelberg MFG, an infinite population of agents play a non-cooperative game and choose their controls to optimize their individual objectives while interacting with the principal and other agents through the population distribution. The principal can influence the mean field Nash equilibrium at the population level through policies, and she optimizes her own objective, which depends on the population distribution. This leads to a bi-level problem between the principal and mean field of agents that cannot be solved using traditional methods for MFGs. We propose a reformulation of this problem as a single-level mean field optimal control problem through a penalization approach, and we prove convergence of the reformulated problem to the original problem. We propose a machine learning method based on neural networks and illustrate it with several examples from the literature. Joint work with Gökçe Dayanikli.

Bio

Mathieu Laurière is an Assistant Professor of Mathematics and Data Science at NYU Shanghai. Prior to joining NYU Shanghai, he was a Postdoctoral Research Associate at Princeton University in the Operations Research and Financial Engineering (ORFE) department and a Visiting Faculty Researcher at Google Brain. He obtained his MS from Sorbonne University and ENS Paris-Saclay and his PhD from the University of Paris. Before joining Princeton University, he was a Postdoctoral Fellow at the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.