In this talk I explain how the theory of optimal transport (OT) can be used to obtain new characterisations of quantities of interest in mathematical finance. I give two examples: I first describe how OT provides a nonparametric measure of association between two random vectors X and Y. It has the interesting property that it is equal to zero if and only if the random vectors are independent, and equal to one if and only if there exists a function f, such that Y=f(X). Secondly, I show how convex order of probability measures can be characterised by OT in general dimensions. This characterisation is based on a combination of Brenier’s theorem and OT duality, and gives a computationally tractable way of checking convex order between arbitrary probability measures.
Bio: Johannes Wiesel is currently an Assistant Professor in the Department of Statistics at Columbia University, and an affiliated member of the Data Science Institute. In summer 2020, he received a PhD from Oxford University under the supervision of Jan Obloj. Johannes’ research focuses on mathematical finance and mathematical statistics with a special emphasis on optimal transport. He is also interested in the robust approach to mathematical finance, which does not start with an a priori model but rather with the information available in the markets.