Optimal martingale transport between radially symmetric marginals in general dimensions

Abstract

We determine the optimal structure of couplings for the \emph{Martingale transport problem} between radially symmetric initial and terminal laws $\mu ,\nu$ on ${\mathbb{R}}^d$ and show the uniqueness of optimizer. Here optimality means that such solutions will minimize the functional $\E |X-Y|^p$ where $0<p\le 1$, and the dimension $d$ is arbitrary.

Some clarifications were made in the proofs

References in corpus (3)

• The Skorokhod embedding problem and its offspring
• A model-free version of the fundamental theorem of asset pricing and the super-replication theorem
• Monotone Martingale Transport Plans and Skorohod Embedding

Cited by in corpus (5)

• On A Mixture Of Brenier and Strassen Theorems
• Computational Methods for Martingale Optimal Transport problems
• Local structure of multi-dimensional martingale optimal transport
• Monotonicity Preserving Transformations of MOT and SEP
• Optimal control of martingales in a radially symmetric environment