Skip to Main content Skip to Navigation
New interface
Preprints, Working Papers, ...

An Explicit Martingale Version of Brenier's Theorem

Abstract : By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry-LaborderePenkner,GalichonHenry-LabordereTouzi}. In this paper, we extend the one-dimensional Brenier's theorem to the present martingale version. We provide the explicit martingale optimal transference plans for a remarkable class of coupling functions corresponding to the lower and upper bounds. These explicit extremal probability measures coincide with the unique left and right monotone martingale transference plans, which were introduced in \cite{BeiglbockJuillet} by suitable adaptation of the notion of cyclic monotonicity. Instead, our approach relies heavily on the (weak) duality result stated in \cite{BeiglbockHenry-LaborderePenkner}, and provides, as a by-product, an explicit expression for the corresponding optimal semi-static hedging strategies. We finally provide an extension to the multiple marginals case.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [42 references]  Display  Hide  Download
Contributor : Nizar Touzi Connect in order to contact the contributor
Submitted on : Wednesday, April 24, 2013 - 6:49:22 AM
Last modification on : Thursday, March 5, 2020 - 6:21:34 PM
Long-term archiving on: : Monday, April 3, 2017 - 9:05:53 AM


Files produced by the author(s)


  • HAL Id : hal-00817179, version 1



Pierre Henry-Labordere, Nizar Touzi. An Explicit Martingale Version of Brenier's Theorem. {date}. ⟨hal-00817179⟩



Record views


Files downloads