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Optimal martingale transport between radially symmetric marginals in general dimensions

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  • Lim, Tongseok

Abstract

We determine the optimal structure of couplings for the Martingale transport problem between radially symmetric initial and terminal laws μ,ν on Rd and show the uniqueness of optimizer. Here optimality means that such solutions will minimize the functional Ef(||X−Y||) where f is concave and strictly increasing, and the dimension d is arbitrary.

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  • Lim, Tongseok, 2020. "Optimal martingale transport between radially symmetric marginals in general dimensions," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1897-1912.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:4:p:1897-1912
    DOI: 10.1016/j.spa.2019.06.005
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    References listed on IDEAS

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    1. Beiglböck, Mathias & Henry-Labordère, Pierre & Touzi, Nizar, 2017. "Monotone martingale transport plans and Skorokhod embedding," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 3005-3013.
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    4. A. Galichon & P. Henry-Labord`ere & N. Touzi, 2014. "A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options," Papers 1401.3921, arXiv.org.
    5. Mathias Beiglböck & Pierre Henry-Labordère & Friedrich Penkner, 2013. "Model-independent bounds for option prices—a mass transport approach," Finance and Stochastics, Springer, vol. 17(3), pages 477-501, July.
    6. Mathias Beiglbock & Pierre Henry-Labord`ere & Friedrich Penkner, 2011. "Model-independent Bounds for Option Prices: A Mass Transport Approach," Papers 1106.5929, arXiv.org, revised Feb 2013.
    7. Gaoyue Guo & Xiaolu Tan & Nizar Touzi, 2015. "Optimal Skorokhod embedding under finitely-many marginal constraints," Papers 1506.04063, arXiv.org, revised Aug 2016.
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    Cited by:

    1. Cox, Alexander M.G. & Robinson, Benjamin A., 2023. "Optimal control of martingales in a radially symmetric environment," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 149-198.

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