4–5 juil. 2019
IRMA in Strasbourg
Fuseau horaire Europe/Paris

8th talk : The inverse transform martingale coupling

5 juil. 2019, 13:10
50m
Salle de conférence (IRMA in Strasbourg)

Salle de conférence

IRMA in Strasbourg

7 rue René Descartes 67084 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.

Documents de présentation

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