An optimal transport based toolbox for mathematical finance
Abstract
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. 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.
About the speaker
No bio is available for this talk.