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Based on the multidimensional irreducible paving of De March & Touzi, we provide a multi-dimensional version of the quasi sure duality for the martingale optimal transport problem, thus extending the result of Beiglb\"ock, Nutz & Touzi.
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A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options
Alfred Galichon, Pierre Henry-Labordere, and Nizar Touzi · 2014
Cited alongside, same era.
Complete duality for martingale optimal transport on the line
Mathias Beiglböck, Marcel Nutz, and Nizar Touzi · 2015
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Measure theory and fine properties of functions
Lawrence Craig Evans and Ronald F Gariepy · 2015
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Mathias Beiglböck, Tongseok Lim, and Jan Oblój · 2017
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Irreducible convex paving for decomposition of multi-dimensional martingale transport plans
Hadrien De March and Nizar Touzi · 2017
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Computational methods for martingale optimal transport problems
Gaoyue Guo and Jan Obloj · 2017
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t.b. (https://math.stackexchange.com/users/5363/t b) · 2017
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