Optimal Transport in Math Finance

Speaker

Xin Zhang
Assistant Professor at New York University.

Title

"Optimal Transport in Math Finance"

Abstract

The problem of optimal transport was first proposed by Gaspard Monge in 1781, and it defines the so-called Wasserstein distance between probability measures. It has gained extreme popularity due to its beautiful interplay between partial differential equations, geometry, and probability theory. Recently, it has become a fundamental tool in applied mathematics such as machine learning and image processing.

In this talk, we will discuss some of its variations that emerge naturally in math finance. In the first part, we will introduce an adapted Wasserstein distance on the space of stochastic processes, designed to quantify differences between stochastic models. This distance respects the underlying information flow of the processes and has become a widely used tool for analyzing the stability of decision making with respect to model perturbations. In the second part, we will present martingale optimal transport, a framework central to robust pricing and model-independent finance. A particularly intriguing example concerns the problem of identifying the “most exciting game”, which can be formulated as a martingale optimal transport problem. We will explain this connection and analyze it in detail.

About Speaker

 Xin Zhang is an Assistant Professor in the Financial and Risk Engineering (FRE) department at New York University. Before joining NYU, he was a University Assistant at the University of Vienna from 2021 to 2024. He earned his Ph.D. in Mathematics from the University of Michigan in 2021, after completing a B.S. in Mathematics at Fudan University in 2016.

Xin Zhang’s research focuses on optimal transport, stochastic analysis and control, particularly their applications in Finance and Machine Learning. His specific interests include viscosity solutions of nonlinear partial differential equations and optimal transport in robust finance.