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(Martingale) Optimal Transport And Anomaly Detection With Neural Networks: A Primal-dual Algorithm

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  • Pierre Henry-Labordere

Abstract

In this paper, we introduce a primal-dual algorithm for solving (martingale) optimal transportation problems, with cost functions satisfying the twist condition, close to the one that has been used recently for training generative adversarial networks. As some additional applications, we consider anomaly detection and automatic generation of financial data.

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  • Pierre Henry-Labordere, 2019. "(Martingale) Optimal Transport And Anomaly Detection With Neural Networks: A Primal-dual Algorithm," Papers 1904.04546, arXiv.org, revised Apr 2019.
    • Handle: RePEc:arx:papers:1904.04546
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    File URL: http://arxiv.org/pdf/1904.04546
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    References listed on IDEAS

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    1. Pierre Henry-Labordère & Nizar Touzi, 2016. "An explicit martingale version of the one-dimensional Brenier theorem," Finance and Stochastics, Springer, vol. 20(3), pages 635-668, July.
    2. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2013. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
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    Cited by:

    1. Stéphane Crépey & Lehdili Noureddine & Nisrine Madhar & Maud Thomas, 2022. "Anomaly Detection on Financial Time Series by Principal Component Analysis and Neural Networks," Working Papers hal-03777995, HAL.
    2. Ariel Neufeld & Julian Sester & Daiying Yin, 2022. "Detecting data-driven robust statistical arbitrage strategies with deep neural networks," Papers 2203.03179, arXiv.org, revised Feb 2024.
    3. Michael Kupper & Max Nendel & Alessandro Sgarabottolo, 2023. "Risk measures based on weak optimal transport," Papers 2312.05973, arXiv.org.
    4. Joshua Zoen-Git Hiew & Tongseok Lim & Brendan Pass & Marcelo Cruz de Souza, 2023. "Geometry of vectorial martingale optimal transport and robust option pricing," Papers 2309.04947, arXiv.org, revised Sep 2023.
    5. St'ephane Cr'epey & Lehdili Noureddine & Nisrine Madhar & Maud Thomas, 2022. "Anomaly Detection on Financial Time Series by Principal Component Analysis and Neural Networks," Papers 2209.11686, arXiv.org, revised Oct 2022.
    6. Ariel Neufeld & Julian Sester, 2021. "Model-free price bounds under dynamic option trading," Papers 2101.01024, arXiv.org, revised Jul 2021.
    7. Hans Buhler & Blanka Horvath & Terry Lyons & Imanol Perez Arribas & Ben Wood, 2020. "A Data-driven Market Simulator for Small Data Environments," Papers 2006.14498, arXiv.org.

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