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Supermartingale Brenier’s Theorem with Full-Marginal Constraint

In: Peter Carr Gedenkschrift Research Advances in Mathematical Finance

Author

Listed:
  • Erhan Bayraktar
  • Shuoqing Deng
  • Dominykas Norgilas

Abstract

We explicitly construct the supermartingale version of the Fréchet– Hoeffding coupling in the setting with infinitely many marginal constraints. Our construction is based on the Markovian iteration of one-period optimal supermartingale couplings. We show that the constructed processes solve the continuous-time supermartingale optimal transport problem for a particular family of (path-dependent) cost functions. The explicit computations are provided in the following three cases: the uniform case, the Bachelier model and the geometric Brownian motion case.

Suggested Citation

  • Erhan Bayraktar & Shuoqing Deng & Dominykas Norgilas, 2023. "Supermartingale Brenier’s Theorem with Full-Marginal Constraint," World Scientific Book Chapters, in: Robert A Jarrow & Dilip B Madan (ed.), Peter Carr Gedenkschrift Research Advances in Mathematical Finance, chapter 17, pages 569-636, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789811280306_0017
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    More about this item

    Keywords

    Mathematical Finance; Quantitative Finance; Option Pricing; Derivatives; No Arbitrage; Asset Price Bubbles; Asset Pricing; Equilibrium; Volatility; Diffusion Processes; Jump Processes; Stochastic Integration; Trading Strategies; Portfolio Theory; Optimization; Securities; Bonds; Commodities; Futures;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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