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A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options

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Cited by:

  1. Y. Dolinsky & H. M. Soner, 2014. "Martingale optimal transport in the Skorokhod space," Papers 1404.1516, arXiv.org, revised Feb 2015.
  2. Beatrice Acciaio & Martin Larsson & Walter Schachermayer, 2016. "The space of outcomes of semi-static trading strategies need not be closed," Papers 1606.00631, arXiv.org.
  3. Mathias Beiglbock & Marcel Nutz & Nizar Touzi, 2015. "Complete Duality for Martingale Optimal Transport on the Line," Papers 1507.00671, arXiv.org, revised Jun 2016.
  4. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglböck & Manu Eder, 2020. "Adapted Wasserstein distances and stability in mathematical finance," Finance and Stochastics, Springer, vol. 24(3), pages 601-632, July.
  5. Sebastian Herrmann & Johannes Muhle-Karbe, 2017. "Model Uncertainty, Recalibration, and the Emergence of Delta-Vega Hedging," Papers 1704.04524, arXiv.org.
  6. Marcel Nutz & Johannes Wiesel & Long Zhao, 2022. "Limits of Semistatic Trading Strategies," Papers 2204.12251, arXiv.org.
  7. Sebastian Herrmann & Florian Stebegg, 2017. "Robust Pricing and Hedging around the Globe," Papers 1707.08545, arXiv.org, revised Apr 2019.
  8. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2014. "Robust Fundamental Theorem for Continuous Processes," Papers 1410.4962, arXiv.org, revised Jul 2015.
  9. Pierre Henry-Labordère & Nizar Touzi, 2016. "An explicit martingale version of the one-dimensional Brenier theorem," Finance and Stochastics, Springer, vol. 20(3), pages 635-668, July.
  10. Ibrahim Ekren & H. Mete Soner, 2016. "Constrained Optimal Transport," Papers 1610.02940, arXiv.org, revised Sep 2017.
  11. Alessandro Doldi & Marco Frittelli, 2020. "Entropy Martingale Optimal Transport and Nonlinear Pricing-Hedging Duality," Papers 2005.12572, arXiv.org, revised Sep 2021.
  12. Marcel Nutz & Johannes Wiesel & Long Zhao, 2023. "Martingale Schrödinger bridges and optimal semistatic portfolios," Finance and Stochastics, Springer, vol. 27(1), pages 233-254, January.
  13. Acciaio, B. & Backhoff-Veraguas, J. & Zalashko, A., 2020. "Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2918-2953.
  14. Mathias Beiglbock & Benjamin Jourdain & William Margheriti & Gudmund Pammer, 2021. "Stability of the Weak Martingale Optimal Transport Problem," Papers 2109.06322, arXiv.org, revised Apr 2022.
  15. Anna Aksamit & Shuoqing Deng & Jan Obl'oj & Xiaolu Tan, 2016. "Robust pricing--hedging duality for American options in discrete time financial markets," Papers 1604.05517, arXiv.org, revised Apr 2017.
  16. Tongseok Lim, 2014. "Optimal martingale transport between radially symmetric marginals in general dimensions," Papers 1412.3530, arXiv.org, revised Feb 2018.
  17. Acciaio, Beatrice & Larsson, Martin & Schachermayer, Walter, 2017. "The space of outcomes of semi-static trading strategies need not be closed," LSE Research Online Documents on Economics 69804, London School of Economics and Political Science, LSE Library.
  18. Linn Engstrom & Sigrid Kallblad & Johan Karlsson, 2024. "Computation of Robust Option Prices via Structured Multi-Marginal Martingale Optimal Transport," Papers 2406.09959, arXiv.org.
  19. Beatrice Acciaio & Mathias Beiglboeck & Gudmund Pammer, 2020. "Weak Transport for Non-Convex Costs and Model-independence in a Fixed-Income Market," Papers 2011.04274, arXiv.org, revised Aug 2023.
  20. Benjamin Jourdain & Gudmund Pammer, 2023. "An extension of martingale transport and stability in robust finance," Papers 2304.09551, arXiv.org.
  21. Christopher W. Miller, 2016. "A Duality Result for Robust Optimization with Expectation Constraints," Papers 1610.01227, arXiv.org.
  22. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," SciencePo Working papers Main hal-03936221, HAL.
  23. Alexander M. G. Cox & Annemarie M. Grass, 2023. "Robust option pricing with volatility term structure -- An empirical study for variance options," Papers 2312.09201, arXiv.org.
  24. Gaoyue Guo & Xiaolu Tan & Nizar Touzi, 2015. "Tightness and duality of martingale transport on the Skorokhod space," Papers 1507.01125, arXiv.org, revised Aug 2016.
  25. Ruodu Wang & Zhenyuan Zhang, 2022. "Simultaneous Optimal Transport," Papers 2201.03483, arXiv.org, revised Dec 2024.
  26. Ethan Anderes & Steffen Borgwardt & Jacob Miller, 2016. "Discrete Wasserstein barycenters: optimal transport for discrete data," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(2), pages 389-409, October.
  27. Anton Kolotilin & Roberto Corrao & Alexander Wolitzky, 2022. "Persuasion with Non-Linear Preferences," Papers 2206.09164, arXiv.org, revised Aug 2022.
  28. Johannes Muhle-Karbe & Marcel Nutz, 2018. "A risk-neutral equilibrium leading to uncertain volatility pricing," Finance and Stochastics, Springer, vol. 22(2), pages 281-295, April.
  29. Johannes Muhle-Karbe & Marcel Nutz, 2016. "A Risk-Neutral Equilibrium Leading to Uncertain Volatility Pricing," Papers 1612.09152, arXiv.org, revised Jan 2018.
  30. Huy N. Chau & Masaaki Fukasawa & Miklos Rasonyi, 2021. "Super-replication with transaction costs under model uncertainty for continuous processes," Papers 2102.02298, arXiv.org.
  31. Tongseok Lim, 2023. "Optimal exercise decision of American options under model uncertainty," Papers 2310.14473, arXiv.org, revised Nov 2023.
  32. Beatrice Acciaio & Antonio Marini & Gudmund Pammer, 2023. "Calibration of the Bass Local Volatility model," Papers 2311.14567, arXiv.org.
  33. Huesmann, Martin & Stebegg, Florian, 2018. "Monotonicity preserving transformations of MOT and SEP," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1114-1134.
  34. Nutz, Marcel & Stebegg, Florian & Tan, Xiaowei, 2020. "Multiperiod martingale transport," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1568-1615.
  35. Gassiat, Paul & Oberhauser, Harald & dos Reis, Gonçalo, 2015. "Root’s barrier, viscosity solutions of obstacle problems and reflected FBSDEs," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4601-4631.
  36. Patrick Cheridito & Michael Kupper & Ludovic Tangpi, 2016. "Duality formulas for robust pricing and hedging in discrete time," Papers 1602.06177, arXiv.org, revised Sep 2017.
  37. Sebastian Herrmann & Johannes Muhle-Karbe & Frank Thomas Seifried, 2017. "Hedging with small uncertainty aversion," Finance and Stochastics, Springer, vol. 21(1), pages 1-64, January.
  38. Alexander M. G. Cox & Sigrid Kallblad, 2015. "Model-independent bounds for Asian options: a dynamic programming approach," Papers 1507.02651, arXiv.org, revised Jul 2016.
  39. Mathias Beiglböck & Alexander M. G. Cox & Martin Huesmann & Nicolas Perkowski & David J. Prömel, 2017. "Pathwise superreplication via Vovk’s outer measure," Finance and Stochastics, Springer, vol. 21(4), pages 1141-1166, October.
  40. Yan Dolinsky & H. Soner, 2014. "Robust hedging with proportional transaction costs," Finance and Stochastics, Springer, vol. 18(2), pages 327-347, April.
  41. Erhan Bayraktar & Christopher W. Miller, 2019. "Distribution‐constrained optimal stopping," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 368-406, January.
  42. Mathias Beiglbock & Alexander M. G. Cox & Martin Huesmann & Nicolas Perkowski & David J. Promel, 2015. "Pathwise super-replication via Vovk's outer measure," Papers 1504.03644, arXiv.org, revised Jul 2016.
  43. Jan Obłój & Johannes Wiesel, 2021. "Distributionally robust portfolio maximization and marginal utility pricing in one period financial markets," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1454-1493, October.
  44. Zhaoxu Hou & Jan Obloj, 2015. "On robust pricing-hedging duality in continuous time," Papers 1503.02822, arXiv.org, revised Jul 2015.
  45. Daniel Krv{s}ek & Gudmund Pammer, 2024. "General duality and dual attainment for adapted transport," Papers 2401.11958, arXiv.org, revised Nov 2024.
  46. Tongseok Lim, 2023. "Replication of financial derivatives under extreme market models given marginals," Papers 2307.00807, arXiv.org.
  47. Julien Claisse & Gaoyue Guo & Pierre Henry-Labordère, 2018. "Some Results on Skorokhod Embedding and Robust Hedging with Local Time," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 569-597, November.
  48. Julien Guyon & Romain Menegaux & Marcel Nutz, 2017. "Bounds for VIX futures given S&P 500 smiles," Finance and Stochastics, Springer, vol. 21(3), pages 593-630, July.
  49. Florian Stebegg, 2014. "Model-Independent Pricing of Asian Options via Optimal Martingale Transport," Papers 1412.1429, arXiv.org.
  50. Anton Kolotilin & Roberto Corrao & Alexander Wolitzky, 2023. "Persuasion and Matching: Optimal Productive Transport," Discussion Papers 2023-12, School of Economics, The University of New South Wales.
  51. Pierre Henry-Labordère, 2019. "(Martingale) Optimal Transport And Anomaly Detection With Neural Networks: A Primal-Dual Algorithm," Working Papers hal-02095222, HAL.
  52. Beatrice Acciaio & Martin Larsson, 2015. "Semi-static completeness and robust pricing by informed investors," Papers 1510.01890, arXiv.org, revised Sep 2016.
  53. Mathias Beiglboeck & Alexander Cox & Martin Huesmann, 2017. "The geometry of multi-marginal Skorokhod Embedding," Papers 1705.09505, arXiv.org.
  54. Stephan Eckstein & Michael Kupper, 2018. "Computation of optimal transport and related hedging problems via penalization and neural networks," Papers 1802.08539, arXiv.org, revised Jan 2019.
  55. Wiesel Johannes & Zhang Erica, 2023. "An optimal transport-based characterization of convex order," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-15, January.
  56. Julio Backhoff-Veraguas & Mathias Beiglbock & Martin Huesmann & Sigrid Kallblad, 2017. "Martingale Benamou--Brenier: a probabilistic perspective," Papers 1708.04869, arXiv.org, revised Jan 2019.
  57. Alessandro Doldi & Marco Frittelli & Emanuela Rosazza Gianin, 2024. "On entropy martingale optimal transport theory," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 1-42, June.
  58. Guo, Gaoyue & Tan, Xiaolu & Touzi, Nizar, 2017. "Tightness and duality of martingale transport on the Skorokhod space," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 927-956.
  59. Alessandro Doldi & Marco Frittelli, 2021. "Real-Valued Systemic Risk Measures," Mathematics, MDPI, vol. 9(9), pages 1-24, April.
  60. Sebastian Herrmann & Johannes Muhle-Karbe & Frank Thomas Seifried, 2016. "Hedging with Small Uncertainty Aversion," Papers 1605.06429, arXiv.org.
  61. Julien Guyon & Romain Menegaux & Marcel Nutz, 2016. "Bounds for VIX Futures given S&P 500 Smiles," Papers 1609.05832, arXiv.org, revised Jun 2017.
  62. Beatrice Acciaio & Alexander M. G. Cox & Martin Huesmann, 2016. "Model-independent pricing with insider information: a Skorokhod embedding approach," Papers 1610.09124, arXiv.org, revised Jun 2020.
  63. Pierre Henry-Labordere, 2019. "(Martingale) Optimal Transport And Anomaly Detection With Neural Networks: A Primal-dual Algorithm," Papers 1904.04546, arXiv.org, revised Apr 2019.
  64. Mathias Beiglboeck & Pierre Henry-Labordere & Nizar Touzi, 2017. "Monotone Martingale Transport Plans and Skorohod Embedding," Papers 1701.06779, arXiv.org.
  65. Gaoyue Guo & Jan Obloj, 2017. "Computational Methods for Martingale Optimal Transport problems," Papers 1710.07911, arXiv.org, revised Apr 2019.
  66. Julio Backhoff-Veraguas & Gudmund Pammer & Walter Schachermayer, 2024. "The Gradient Flow of the Bass Functional in Martingale Optimal Transport," Papers 2407.18781, arXiv.org.
  67. Asaf Cohen & Yan Dolinsky, 2022. "A scaling limit for utility indifference prices in the discretised Bachelier model," Finance and Stochastics, Springer, vol. 26(2), pages 335-358, April.
  68. Stephan Eckstein & Gaoyue Guo & Tongseok Lim & Jan Obloj, 2019. "Robust pricing and hedging of options on multiple assets and its numerics," Papers 1909.03870, arXiv.org, revised Oct 2020.
  69. Lim, Tongseok, 2020. "Optimal martingale transport between radially symmetric marginals in general dimensions," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1897-1912.
  70. David Hobson & Dominykas Norgilas, 2019. "Robust bounds for the American put," Finance and Stochastics, Springer, vol. 23(2), pages 359-395, April.
  71. Marcel Nutz & Johannes Wiesel, 2024. "On the Martingale Schr\"odinger Bridge between Two Distributions," Papers 2401.05209, arXiv.org.
  72. Dylan Possamai & Xiaolu Tan & Chao Zhou, 2015. "Stochastic control for a class of nonlinear kernels and applications," Papers 1510.08439, arXiv.org, revised Jul 2017.
  73. Maximilien Germain & Huyên Pham & Xavier Warin, 2022. "A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection," Post-Print hal-03498263, HAL.
  74. Daniel Bartl & Michael Kupper & David J. Prömel & Ludovic Tangpi, 2019. "Duality for pathwise superhedging in continuous time," Finance and Stochastics, Springer, vol. 23(3), pages 697-728, July.
  75. 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.
  76. Luciano Campi & Claude Martini, 2016. "On the support of extremal martingale measures with given marginals: the countable case," Papers 1607.07197, arXiv.org, revised Mar 2019.
  77. Joshua Zoen-Git Hiew & Tongseok Lim & Brendan Pass & Marcelo Cruz de Souza, 2023. "Geometry of vectorial martingale optimal transport and robust option pricing," Papers 2309.04947, arXiv.org, revised Sep 2023.
  78. Benjamin Jourdain & Gilles Pagès, 2022. "Convex Order, Quantization and Monotone Approximations of ARCH Models," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2480-2517, December.
  79. 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..
  80. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2017. "Robust Fundamental Theorem for Continuous Processes," Post-Print hal-01076062, HAL.
  81. Asaf Cohen & Yan Dolinsky, 2021. "A Scaling Limit for Utility Indifference Prices in the Discretized Bachelier Model," Papers 2102.11968, arXiv.org, revised Mar 2022.
  82. Erhan Bayraktar & Gu Wang, 2018. "Quantile Hedging in a semi-static market with model uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(2), pages 197-227, April.
  83. Tavin, Bertrand, 2015. "Detection of arbitrage in a market with multi-asset derivatives and known risk-neutral marginals," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 158-178.
  84. Daniel Bartl & Michael Kupper & David J. Promel & Ludovic Tangpi, 2017. "Duality for pathwise superhedging in continuous time," Papers 1705.02933, arXiv.org, revised Apr 2019.
  85. Nassif Ghoussoub & Young-Heon Kim & Tongseok Lim, 2017. "Optimal Brownian Stopping between radially symmetric marginals in general dimensions," Papers 1711.02784, arXiv.org.
  86. David Hobson & Martin Klimmek, 2015. "Robust price bounds for the forward starting straddle," Finance and Stochastics, Springer, vol. 19(1), pages 189-214, January.
  87. Beatrice Acciaio & Martin Larsson & Walter Schachermayer, 2017. "The space of outcomes of semi-static trading strategies need not be closed," Finance and Stochastics, Springer, vol. 21(3), pages 741-751, July.
  88. Mario Ghossoub & Jesse Hall & David Saunders, 2020. "Maximum Spectral Measures of Risk with given Risk Factor Marginal Distributions," Papers 2010.14673, arXiv.org.
  89. Julien Claisse & Gaoyue Guo & Pierre Henry-Labordere, 2015. "Some Results on Skorokhod Embedding and Robust Hedging with Local Time," Papers 1511.07230, arXiv.org, revised Oct 2017.
  90. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2015. "Model-free Superhedging Duality," Papers 1506.06608, arXiv.org, revised May 2016.
  91. Zhengqing Zhou & Jose Blanchet & Peter W. Glynn, 2021. "Distributionally Robust Martingale Optimal Transport," Papers 2106.07191, arXiv.org, revised Nov 2021.
  92. Julio Backhoff & Gregoire Loeper & Jan Obloj, 2024. "Geometric Martingale Benamou-Brenier transport and geometric Bass martingales," Papers 2406.04016, arXiv.org, revised Feb 2025.
  93. Marcel Nutz & Florian Stebegg & Xiaowei Tan, 2017. "Multiperiod Martingale Transport," Papers 1703.10588, arXiv.org, revised May 2019.
  94. Julio Backhoff-Veraguas & Gudmund Pammer, 2019. "Stability of martingale optimal transport and weak optimal transport," Papers 1904.04171, arXiv.org, revised Dec 2020.
  95. Marcel Nutz & Johannes Wiesel & Long Zhao, 2023. "Limits of semistatic trading strategies," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 185-205, January.
  96. Mathias Beiglbock & Marcel Nutz & Florian Stebegg, 2019. "Fine Properties of the Optimal Skorokhod Embedding Problem," Papers 1903.03887, arXiv.org, revised Apr 2020.
  97. Henry-Labordère, Pierre & Tan, Xiaolu & Touzi, Nizar, 2016. "An explicit martingale version of the one-dimensional Brenier’s Theorem with full marginals constraint," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2800-2834.
  98. Nabil Kahalé, 2017. "Superreplication of Financial Derivatives via Convex Programming," Management Science, INFORMS, vol. 63(7), pages 2323-2339, July.
  99. Marcel Nutz & Johannes Wiesel & Long Zhao, 2022. "Martingale Schr\"odinger Bridges and Optimal Semistatic Portfolios," Papers 2204.12250, arXiv.org.
  100. Acciaio, Beatrice & Larsson, Martin, 2017. "Semi-static completeness and robust pricing by informed investors," LSE Research Online Documents on Economics 68502, London School of Economics and Political Science, LSE Library.
  101. Veraguas, Julio Backhoff & Beiglböck, Mathias & Eder, Manu & Pichler, Alois, 2020. "Fundamental properties of process distances," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5575-5591.
  102. Beiglböck, Mathias & Henry-Labordère, Pierre & Touzi, Nizar, 2017. "Monotone martingale transport plans and Skorokhod embedding," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 3005-3013.
  103. Marcel Nutz, 2014. "Superreplication under model uncertainty in discrete time," Finance and Stochastics, Springer, vol. 18(4), pages 791-803, October.
  104. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglbock & Manu Eder, 2019. "Adapted Wasserstein Distances and Stability in Mathematical Finance," Papers 1901.07450, arXiv.org, revised May 2020.
  105. Ariel Neufeld & Julian Sester, 2021. "A deep learning approach to data-driven model-free pricing and to martingale optimal transport," Papers 2103.11435, arXiv.org, revised Dec 2022.
  106. Acciaio, B. & Backhoff-Veraguas, J. & Zalashko, A., 2020. "Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization," LSE Research Online Documents on Economics 101864, London School of Economics and Political Science, LSE Library.
  107. Dolinsky, Yan & Soner, H. Mete, 2015. "Martingale optimal transport in the Skorokhod space," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3893-3931.
  108. Huy N. Chau & Masaaki Fukasawa & Miklós Rásonyi, 2022. "Super‐replication with transaction costs under model uncertainty for continuous processes," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1066-1085, October.
  109. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," Working Papers hal-03936221, HAL.
  110. Luca De Gennaro Aquino & Carole Bernard, 2019. "Bounds on Multi-asset Derivatives via Neural Networks," Papers 1911.05523, arXiv.org, revised Nov 2020.
  111. Beatrice Acciaio & Mathias Beiglböck & Gudmund Pammer, 2021. "Weak transport for non‐convex costs and model‐independence in a fixed‐income market," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1423-1453, October.
  112. Sebastian Herrmann & Johannes Muhle-Karbe, 2017. "Model uncertainty, recalibration, and the emergence of delta–vega hedging," Finance and Stochastics, Springer, vol. 21(4), pages 873-930, October.
  113. Patrick Cheridito & Matti Kiiski & David J. Promel & H. Mete Soner, 2019. "Martingale optimal transport duality," Papers 1904.04644, arXiv.org, revised Nov 2020.
  114. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2020. "Model-free bounds for multi-asset options using option-implied information and their exact computation," Papers 2006.14288, arXiv.org, revised Jan 2022.
  115. Gaoyue Guo & Xiaolu Tan & Nizar Touzi, 2015. "Optimal Skorokhod embedding under finitely-many marginal constraints," Papers 1506.04063, arXiv.org, revised Aug 2016.
  116. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2023. "Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Their Exact Computation," Management Science, INFORMS, vol. 69(4), pages 2051-2068, April.
  117. Steffen Borgwardt, 2022. "An LP-based, strongly-polynomial 2-approximation algorithm for sparse Wasserstein barycenters," Operational Research, Springer, vol. 22(2), pages 1511-1551, April.
  118. Haiyan Liu & Bin Wang & Ruodu Wang & Sheng Chao Zhuang, 2023. "Distorted optimal transport," Papers 2308.11238, arXiv.org.
  119. Zhaoxu Hou & Jan Obłój, 2018. "Robust pricing–hedging dualities in continuous time," Finance and Stochastics, Springer, vol. 22(3), pages 511-567, July.
  120. Marcel Nutz & Florian Stebegg, 2016. "Canonical Supermartingale Couplings," Papers 1609.02867, arXiv.org, revised Nov 2017.
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