# Monotonicity preserving transformations for martingale optimal transport and the Skorokhod embedding problem

## Martin Huesmann

created by trevisan on 02 Sep 2016

7 sep 2016 -- 14:00   [open in google calendar]

Aula Riunioni - Dipartimento Matematica Pisa

Abstract.

There are many transformations mapping martingales into martingales, e.g.\ $M_t\mapsto M_t^2-\langle M\rangle_t$. However, looking at solutions to the martingale optimal transport problem it turns out that there are only very few transformations that map optimal martingale couplings into optimal martingale couplings. After a short introduction to and review of the state of the art of martingale optimal transport we will give a characterization of all these monotonicity preserving transformations. In particular, these transformation reveal certain symmetries between different solutions to the martingale optimal transport problem. Moreover, we will show that the transport approach to Skorokhod embedding is a powerful tool to study martingale optimal transport and, in turn, that the new symmetries for martingale optimal transport disclose symmetries for solutions to the Skorokhod embedding problem. (based on joint work with Florian Stebegg)

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