Machine Learning in Finance

Speaker: Grégoire Loeper (BNP Paribas Global Markets, genOTC)

Date/Time: Wednesday, 10/15, 7:00pm CET (10:00am PST, 1:00pm EST)

Title: Optimal Transport Approach for Generative Diffusion Models

Abstract: The Schrodinger problem can be recast as an optimal transport problem where the diffusion coefficient is fixed and the control is the drift. It was originally stated as a relative entropy minimization under marginal constraints, and can therefore be solved by the celebrated Sinkhorn algorithm.

The Bass martingale problem on the other hand can be stated as an optimal transport problem where the diffusion coefficient is the control and the drift is set to zero (martingale contraint).

It was also recently found that it could be solved by a measure preserving version of the Sinkhorn algorithm, the MPMS algorithm introduced by Joseph, Loeper, Obloj in https://arxiv.org/abs/2310.13797.

It turns out that there is a continuum of optimal transport problems that link Bass and Schrodinger which we name the Schrodinger Bass Bridges (SBB). These problems lead to Sinkhorn like systems at optimality, and can also be solved efficiently even in high dimensions (e.g. for images).

This is based on joint works with A. Alouadi (UPC, BNP-PAR), P. Henry-Labordère (Qube RT), H. Pham (Ecole Polytechnique), O. Mazhar (UPC, LPSM)  and N. Touzi  (NYU), B. Joesph (genOTC), J. Obloj (University of Oxford).