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Maximal Martingale Wasserstein Inequality

Author

Listed:
  • Benjamin Jourdain

    (MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique, CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées)

  • Kexin Shao

    (MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique, CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this note, we complete the analysis of the Martingale Wasserstein Inequality started in [5] by checking that this inequality fails in dimension d ≥ 2 when the integrability parameter ρ belongs to [1, 2) while a stronger Maximal Martingale Wasserstein Inequality holds whatever the dimension d when ρ ≥ 2.

Suggested Citation

  • Benjamin Jourdain & Kexin Shao, 2024. "Maximal Martingale Wasserstein Inequality," Post-Print hal-04241070, HAL.
    • Handle: RePEc:hal:journl:hal-04241070
    DOI: 10.1214/24-ECP593
    Note: View the original document on HAL open archive server: https://hal.science/hal-04241070v1
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    References listed on IDEAS

    as
    1. Mathias Beiglbock & Benjamin Jourdain & William Margheriti & Gudmund Pammer, 2021. "Stability of the Weak Martingale Optimal Transport Problem," Papers 2109.06322, arXiv.org, revised Apr 2022.
    2. David Hobson & Martin Klimmek, 2015. "Robust price bounds for the forward starting straddle," Finance and Stochastics, Springer, vol. 19(1), pages 189-214, January.
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