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In this paper, we introduce a primal-dual algorithm for solving (martingale) optimal transportation problems, with cost functions satisfying the twist condition, close to the one that has been used recently for training generative adversarial networks.
1902
Earlier work this paper cites.
Villani, C. : Topics in Optimal Transportation
2003
Earlier work this paper cites.
Chambolle, A., Pock, T. : A first-order primal-dual algorithm for convex problems with applications to imaging
2011
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Beiglböck, M., Henry-Labordère, P., Penkner, F. : Model-independent Bounds for Option Prices: A Mass-Transport Approach
2013
Earlier work this paper cites.
Henry-Labordère, P. : Automated Option Pricing: Numerical Method
2013
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Galichon, A., Henry-Labordère, P., Touzi, N. : A stochastic control approach to no-arbitrage bounds given marginals, with an application to Lookback options
2014
Cited alongside, same era.
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., Bengio, Y. : Generative Adversarial Networks
2014
Cited alongside, same era.
Kingma, D.P., Ba, J. : Adam: A Method for Stochastic Optimization
2015
Cited alongside, same era.
Arjovsky, M., Chintala, S., Bottou, L. : Wasserstein GAN
Cited in the paper.
Cited in the paper.
Cuturi, M. : Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances
Cited in the paper.
De March, A. : Entropic resolution for multi-dimensional optimal transport
Cited in the paper.
De March, A. : Local structure of multi-dimensional martingale optimal transport
Cited in the paper.
Cited in the paper.
Guo, G., Jan Obloj, J. : Computational Methods for Martingale Optimal Transport problems
Cited in the paper.
Cited in the paper.
Beiglböck, M., Juillet, N. : On a problem of optimal transport under marginal martingale constraints
2016
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Genevay, A., Cuturi, M., Peyr´e, G., Bach, F. : Stochastic optimization for large scale optimal transport
2016
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Henry-Labordère, P., Touzi, N. : An Explicit Martingale Version of Brenier’s Theorem
2016
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Henry-Labordère, P : Model-free Hedging: A Martingale optimal transportation viewpoint
2017
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