Abstract

Recent advances in generative modeling rely on learning stochastic dynamics that transform simple probability distributions into complex data. In this talk, I present a new framework based on an optimal transport problem on path space that bridges two classical constructions in probability: the Schrödinger bridge and Bass martingale transport.

The resulting Schrödinger–Bass bridge yields a diffusion process whose drift and volatility are both learned from data, providing a flexible way to model stochastic dynamics.

 

I first introduce the theoretical foundations of this approach and illustrate its use in generative modeling for image synthesis. I then extend the framework to joint time-series distributions, leading to a new model called SBBTS (Schrödinger Bridge Bass for Time Series).

Applications to financial data show that SBBTS can recover key stochastic volatility features and generate synthetic time series that improve forecasting performance and risk-adjusted returns when used for data augmentation.

 

Biography

Huyên Pham is Full Professor of Applied Mathematics at École Polytechnique, where he leads the Mathematical Finance group at the Centre de Mathématiques Appliquées (CMAP) and directs the Chairs Machine Learning and Systematic Methods (MLSM) and Risques Financiers.

Prior to joining École Polytechnique, he was Professor of Mathematics at Université Paris Cité. His research interests lie at the interface of stochastic control, probability, quantitative finance, and machine learning, with recent work exploring connections between  optimal transport, generative diffusion  models, and reinforcement learning for complex systems and large-population dynamics.

 

He is the author of more than 120 scientific publications, including the monograph Continuous-Time Stochastic Control and Optimization with Financial Applications. He was appointed to the Institut Universitaire de France in 2006 and received the Louis Bachelier Prize of the French Academy of Sciences in 2007. He currently serves as President of the Bachelier Finance Society and Editor-in-Chief of the SIAM Journal on Control and Optimization.