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Monotonicity preserving transformations of MOT and SEP

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  • Huesmann, Martin
  • Stebegg, Florian

Abstract

Recently, Beiglböck and Juillet (2016) and Beiglböck et al. (2015) established that optimizers to the martingale optimal transport problem (MOT) are concentrated on c-monotone sets. In this article we characterize monotonicity preserving transformations revealing certain symmetries between optimizers of MOT for different cost functions. Due to the intimate connection of MOT and the Skorokhod embedding problem (SEP) these transformations are also monotonicity preserving and disclose symmetries for certain solutions to the optimal SEP. Furthermore, the SEP picture allows to easily understand the geometry of these transformations once we have established the SEP counterparts to the known solutions of MOT based on the monotonicity principle for SEP which in turn allows to directly read off the structure of the MOT optimizers.

Suggested Citation

  • Huesmann, Martin & Stebegg, Florian, 2018. "Monotonicity preserving transformations of MOT and SEP," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1114-1134.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:4:p:1114-1134
    DOI: 10.1016/j.spa.2017.07.005
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    References listed on IDEAS

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    8. Mathias Beiglböck & Alexander M. G. Cox & Martin Huesmann & Nicolas Perkowski & David J. Prömel, 2017. "Pathwise superreplication via Vovk’s outer measure," Finance and Stochastics, Springer, vol. 21(4), pages 1141-1166, October.
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    Cited by:

    1. Nicole Bäuerle & Daniel Schmithals, 2019. "Martingale optimal transport in the discrete case via simple linear programming techniques," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(3), pages 453-476, December.
    2. Mathias Beiglbock & Marcel Nutz & Florian Stebegg, 2019. "Fine Properties of the Optimal Skorokhod Embedding Problem," Papers 1903.03887, arXiv.org, revised Apr 2020.

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