Prediction with expert advice is one of the fundamental problems in online learning and sequential decision making with an exploration-exploitation trade-off. The problem is often analyzed in adversarial settings and has wide-ranging applications, including risk management, security training, and betting markets. 

In this talk, we will explore the long time behavior of prediction problems using PDEs. In the first part, we consider a scenario where both the adversary and the forecaster have full observation of what happens. In this case, the asymptotic behavior is described  by  a nonlinear degenerate parabolic equation.  Subsequently, we address a situation where the forecaster only has access to partial information, leading to a PDE defined on Wasserstein space. We will also discuss a comparison principle relevant to this latter equation.

Bio:   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.

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.