6:00 PM Seminar Begins

7:30 PM Reception

Hybrid Event

Fordham University

McNally Amphitheater

140 West 62nd Street

New York, NY 10023

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Abstract:

Generative models aim to approximate an unknown probability distribution in a high dimensional space using a finite sample of independent draws. Motivated by variance-preserving score-based diffusion models, we introduce a new diffusion-based transport plan on path space that is optimal with respect to a criterion combining entropy minimization and stabilization of the quadratic variation. The resulting transport plan can be interpreted as an interpolation between the Schrödinger bridge and the Bass solution from martingale optimal transport. The proposed method has a computational complexity comparable to that of state-of-the-art approaches, while yielding a significant improvement in generation quality.

Bio:

Nizar Touzi is an applied mathematician with expertise in financial engineering and decision modeling. He is currently Professor at New York University, Tandon School of Engineering, Chair of the Department of Finance and Risk Engineering at the Tandon School of Engineering. He was previously Professor at the Department of Applied Mathematics of Ecole Polytechnique in France from 2006 to 2023 where he acted as Chair from 2014 to 2017 and head of the doctoral school from 2020 to 2023.

Nizar has contributed to financial mathematics, optimal control, martingale optimal transport and backward stochastic differential equations which serve as a major tool for the stochastic control of non-Markovian models, for stochastic differential games, and for various applications in risk management and decision models under agent interactions. He received the Louis Bachelier Natixis prize of the French Academy of Sciences in 2012, the Paris Europlace prize of Best Young Researcher in Finance in 2007, an ERC advanced grant 2012-2017, and has been an invited session speaker at the International Congress of Mathematicians in Hyderabad 2010.