I will review three extensions of the classical Monge-Kantorovich framework of optimal transport theory which are designed to cover three specific applications in different fields. The first one ‘Vector Quantile Regression’ (Carlier, Chernozhukov and G, Ann Statistics 2016) allows for a multivariate version of quantile regression, an important tool for data representation in statistics. The second one, ‘Optimal Martingale Transport’ (G, Henry-Labordère and Touzi, Ann Appl Proba 2014) allows for model-free pricing of a class of derivatives in finance and provides variational solutions to the Skorohod embedding problem. The third one, ‘Equilibrium Transport’ (G, Kominers and Weber, J Political Economy 2018) allows for applications to matching models in economics. This talk, at the intersection of mathematics, economics and computation, will be informal and self-contained.
Alfred Galichon is Professor of Economics at the College of Arts & Science of NYU, Professor of Mathematics at the Courant Institute of NYU, and the director of NYU-Paris. His research interests span widely across theoretical, computational and empirical questions and include econometrics, microeconomic theory, and data science. He is one of the pioneers of the use of optimal transport theory in econometrics, and the author of a monograph on the topic, Optimal Transport Methods in Economics (Princeton, 2016), as well as of an open-source statistical software implementing these techniques, TraME. Among his research contributions, he has co-invented vector quantile regression, a multivariate statistical regression technique; affinity estimation, a method for inferring preferences in matching markets; and the mass transport approach to demand inversion, a class of methods to invert multinomial choice models. He is also among the early contributors to optimal martingale transport theory, and more recently to equilibrium transport theory. He is the author of close to forty research articles that have appeared in journals such as the Annals of Statistics, the Journal of Political Economy, Econometrica, and the Review of Economic Studies. He is a co-editor of Economic Theory and he has served as the principal investigator of grants under the European Research Council (ERC) and the National Science Foundation (NSF). Alfred Galichon is also interested in designing innovative educational experiences. At NYU he has created two novel courses drawing students from economics, mathematics and data science, and he is frequently invited to give lecture series in other universities. Recently he has initiated the ‘math+econ+code’ masterclasses, a series of week-long immersive classes at the intersection between mathematics, economics and computation. Prof. Galichon holds a Ph.D. in economics from Harvard University, an engineering degree from Ecole Polytechnique a masters degree from Ecole des Mines de Paris.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai