Variational analysis in the Wasserstein space of stochastic processes

The project's focus is on model uncertainty in mathematical finance. It addresses the following questions: 

-How can one act optimally in a financial market when reality deviates from model assumptions? -How can one measure these deviations, and more generally: -How can one quantify model uncertainty? 

The project's approach will be based on optimal transport of stochastic processes (OTSP).  Amplified by computational advances, optimal transport (OT) theory has become an indispensable tool with far-reaching applications. Research in this area currently faces two main challenges:  

-due to the added time component, the analytic structure of OTSP spaces is more complex than that of OT spaces, -OTSP problems have high computational cost. 

This project offers a novel approach to addressing both of these problems simultaneously, through a variational analysis in the Wasserstein space of stochastic processes.