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Entropy martingale optimal transport and nonlinear pricing–hedging duality

Author

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  • Alessandro Doldi

    (Università degli Studi di Milano)

  • Marco Frittelli

    (Università degli Studi di Milano)

Abstract

The objective of this paper is to develop a duality between a novel entropy martingale optimal transport (EMOT) problem and an associated optimisation problem. In EMOT, we follow the approach taken in the entropy optimal transport (EOT) problem developed in Liero et al. (Invent. Math. 211:969–1117, 2018), but we add the constraint, typical of martingale optimal transport (MOT) theory, that the infimum of the cost functional is taken over martingale probability measures. In the associated problem, the objective functional, related via Fenchel conjugacy to the entropic term in EMOT, is no longer linear as in (martingale) optimal transport. This leads to a novel optimisation problem which also has a clear financial interpretation as a nonlinear subhedging problem. Our theory allows us to establish a nonlinear robust pricing–hedging duality which also covers a wide range of known robust results. We also focus on Wasserstein-induced penalisations and study how the duality is affected by variations in the penalty terms, with a special focus on the convergence of EMOT to the extreme case of MOT.

Suggested Citation

  • Alessandro Doldi & Marco Frittelli, 2023. "Entropy martingale optimal transport and nonlinear pricing–hedging duality," Finance and Stochastics, Springer, vol. 27(2), pages 255-304, April.
    • Handle: RePEc:spr:finsto:v:27:y:2023:i:2:d:10.1007_s00780-023-00498-x
    DOI: 10.1007/s00780-023-00498-x
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    References listed on IDEAS

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    More about this item

    Keywords

    Martingale optimal transport problem; Entropy optimal transport problem; Pricing–hedging duality; Robust finance; Pathwise finance;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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