Supermartingale Brenier’s Theorem with Full-Marginal Constraint

Erhan Bayraktar, Shuoqing Deng and Dominykas Norgilas

Chapter 17 in Peter Carr Gedenkschrift:Research Advances in Mathematical Finance, 2023, pp 569-636 from World Scientific Publishing Co. Pte. Ltd.

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.

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 (search for similar items in EconPapers)
JEL-codes: C02 C6 (search for similar items in EconPapers)
Date: 2023
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Working Paper: Supermartingale Brenier's Theorem with full-marginals constraint (2022)
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