Eight or Nine Talks on Contemporary Optimal Transport Problems

8th talk : The inverse transform martingale coupling

5 juil. 2019, 13:10

50m

Salle de conférence (IRMA in Strasbourg)

Orateur

Benjamin Jourdain (Université Paris-Est)

Description

We exhibit a new martingale coupling between two probability measures $\mu$ and $\nu$ in convex order on the real line. This coupling is explicit in terms of the integrals of the positive and negative parts of the difference between the quantile functions of $\mu$ and $\nu$. The integral of $|y-x|$ with respect to this coupling is smaller than twice the Wasserstein distance with index one between $\mu$ and $\nu$. When the comonotonous coupling between $\mu$ and $\nu$ is given by a map $T$, it minimizes the integral of $|y-T(x)|$ among all martingales couplings.