David Sprott Distinguished Lecture by Hans Föllmer

Optimal Transport, Entropy, and Risk Measures on Wiener space

We discuss the interplay between entropy, large deviations, and optimal couplings on Wiener space.

In particular we prove a new rescaled version of Talagrand’s transport inequality. As an application, we consider rescaled versions of the entropic risk measure which are sensitive to risks in the fine structure of Brownian paths.