Quantifying Distributional Model Risk in Marginal Problems via Optimal Transport

Published Online:https://doi.org/10.1287/moor.2024.0557

References

  • [1] Adjaho C, Christensen T (2022) Externally valid policy choice. Preprint, submitted May 11, https://arxiv.org/abs/2205.05561.Google Scholar
  • [2] Awasthi P, Jung C, Morgenstern J (2022) Distributionally robust data join. Preprint, submitted February 11, https://arxiv.org/abs/2202.05797.Google Scholar
  • [3] Bartl D, Drapeau S, Tangpi L (2020) Computational aspects of robust optimized certainty equivalents and option pricing. Math. Finance 30(1):287–309.CrossrefGoogle Scholar
  • [4] Bertsekas DP, Shreve SE (1978) Stochastic Optimal Control. The Discrete-Time Case, Optimization and Neural Computation Series (Athena Scientific, Belmont, MA).Google Scholar
  • [5] Blanchet J, Murthy K (2019) Quantifying distributional model risk via optimal transport. Math. Oper. Res. 44(2):565–600.LinkGoogle Scholar
  • [6] Blanchet J, Murthy K, Nguyen VA (2021) Statistical analysis of Wasserstein distributionally robust estimators. Carlsson JG, Shier D, Greenberg HJ, eds. Tutorials in Operations Research: Emerging Optimization Methods and Modeling Techniques with Applications (INFORMS, Catonsville, MD), 227–254.LinkGoogle Scholar
  • [7] Chen X, Hong H, Tarozzi A (2008) Semiparametric efficiency in GMM models with auxiliary data. Ann. Statist. 36(2):808–843.CrossrefGoogle Scholar
  • [8] Chen M, Du W, Tang Y, Jin Y, Yen GG (2022) A decomposition method for both additively and non-additively separable problems. IEEE Trans. Evolutionary Computat. 27(6):1720–1734.CrossrefGoogle Scholar
  • [9] Cheridito P, Eckstein S (2023) Optimal transport and Wasserstein distances for causal models. Preprint, submitted March 24, https://arxiv.org/abs/2303.14085.Google Scholar
  • [10] Doan XV, Li X, Natarajan K (2015) Robustness to dependency in portfolio optimization using overlapping marginals. Oper. Res. 63(6):1468–1488.LinkGoogle Scholar
  • [11] Eckstein S, Kupper M, Pohl M (2020) Robust risk aggregation with neural networks. Math. Finance 30(4):1229–1272.CrossrefGoogle Scholar
  • [12] Embrechts P, Puccetti G (2010) Bounds for the sum of dependent risks having overlapping marginals. J. Multivariate Anal. 101(1):177–190.CrossrefGoogle Scholar
  • [13] Embrechts P, Höing A, Juri A (2003) Using copulae to bound the Value-at-Risk for functions of dependent risks. Finance Stochastics 7(2):145–167.CrossrefGoogle Scholar
  • [14] Embrechts P, Höing A, Puccetti G (2005) Worst VaR scenarios. Insurance Math. Econom. 37(1):115–134.CrossrefGoogle Scholar
  • [15] Embrechts P, Puccetti G, Rüschendorf L (2013) Model uncertainty and VaR aggregation. J. Banking Finance 37(8):2750–2764.CrossrefGoogle Scholar
  • [16] Ennaji H, Mérigot Q, Nenna L, Pass B (2022) Robust risk management via multi-marginal optimal transport. Preprint, submitted November 14, https://arxiv.org/abs/2211.07694.Google Scholar
  • [17] Fan K (1953) Minimax theorems. Proc. Natl. Acad. Sci. USA 39(1):42–47.CrossrefGoogle Scholar
  • [18] Fan Y, Park SS (2009) Partial identification of the distribution of treatment effects and its confidence sets. Li Q, Racine JS, eds. Advances in Econometrics, vol. 25 (Emerald Group Publishing Limited, Leeds, UK), 3–70.Google Scholar
  • [19] Fan Y, Park SS (2010) Sharp bounds on the distribution of treatment effects and their statistical inference. Econom. Theory 26(3):931–951.CrossrefGoogle Scholar
  • [20] Fan Y, Park SS (2012) Confidence intervals for the quantile of treatment effects in randomized experiments. J. Econometrics 167(2):330–344.CrossrefGoogle Scholar
  • [21] Fan Y, Wu J (2009) Partial identification of the distribution of treatment effects in switching regime models and its confidence sets. Rev. Econom. Stud. 77(3):1002–1041.CrossrefGoogle Scholar
  • [22] Fan Y, Guerre E, Zhu D (2017) Partial identification of functionals of the joint distribution of “potential outcomes.” J. Econometrics 197(1):42–59.CrossrefGoogle Scholar
  • [23] Firpo S, Ridder G (2019) Partial identification of the treatment effect distribution and its functionals. J. Econometrics 213(1):210–234.CrossrefGoogle Scholar
  • [24] Frank MJ, Nelsen RB, Schweizer B (1987) Best-possible bounds for the distribution of a sum — A problem of Kolmogorov. Probab. Theory Related Fields 74(2):199–211.CrossrefGoogle Scholar
  • [25] Gao R, Kleywegt A (2022) Distributionally robust stochastic optimization with Wasserstein distance. Math. Oper. Res. 48(2):603–655.LinkGoogle Scholar
  • [26] Ghossoub M, Hall J, Saunders D (2023) Maximum spectral measures of risk with given risk factor marginal distributions. Math. Oper. Res. 48(2):1158–1182.LinkGoogle Scholar
  • [27] Graham BS, de Xavier Pinto CC, Egel D (2016) Efficient estimation of data combination models by the method of auxiliary-to-study tilting (AST). J. Bus. Econom. Statist. 34(2):288–301.CrossrefGoogle Scholar
  • [28] Jiang Y (2024) Duality of causal distributionally robust optimization: The discrete-time case. Preprint, submitted January 29, https://arxiv.org/abs/2401.16556.Google Scholar
  • [29] Kallus N, Mao X, Zhou A (2022) Assessing algorithmic fairness with unobserved protected class using data combination. Management Sci. 68(3):1959–1981.LinkGoogle Scholar
  • [30] Kellerer HG (1964) Verteilungsfunktionen mit gegebenen marginalverteilungen. Z. Wahrscheinlichkeitstheorie Verw. Gebiete 3(3):247–270.CrossrefGoogle Scholar
  • [31] Kellerer HG (1984) Duality theorems for marginal problems. Z Wahrscheinlichkeitstheorie Verw. Gebiete 67(4):399–432.CrossrefGoogle Scholar
  • [32] Kent CR (2021) Optimization in the space of measures: New techniques from optimal transport. PhD dissertation, Stanford University, Stanford, CA.Google Scholar
  • [33] Kido D (2022) Distributionally robust policy learning with Wasserstein distance. Preprint, submitted May 10, https://arxiv.org/abs/2205.04637.Google Scholar
  • [34] Kitagawa T, Tetenov A (2018) Who should be treated? Empirical welfare maximization methods for treatment choice. Econometrica 86(2):591–616.CrossrefGoogle Scholar
  • [35] Kuhn D, Esfahani PM, Nguyen VA, Shafieezadeh-Abadeh S (2019) Wasserstein distributionally robust optimization: Theory and applications in machine learning. Netessine S, Shier D, Greenberg HJ, eds. Operations Research and Management Science in the Age of Analytics (INFORMS, Catonsville, MD), 130–166.LinkGoogle Scholar
  • [36] Makarov GD (1982) Estimates for the distribution function of a sum of two random variables when the marginal distributions are fixed. Theory Probab. Appl. 26(4):803–806.CrossrefGoogle Scholar
  • [37] Mehta R, Kline J, Lokhande VS, Fung G, Singh V (2023) Efficient discrete multi marginal optimal transport regularization. 11th Internat. Conf. Learn. Representations (ICLR, Appleton, WI).Google Scholar
  • [38] Mo W, Qi Z, Liu Y (2020) Learning optimal distributionally robust individualized treatment rules. J. Amer. Statist. Assoc. 116(534):659–674.CrossrefGoogle Scholar
  • [39] Nenna L, Pass B (2022) An ODE characterisation of multi-marginal optimal transport. Preprint, submitted December 23, https://arxiv.org/abs/2212.12492.Google Scholar
  • [40] Pass B (2010) Uniqueness and Monge solutions in the multi-marginal optimal transportation problem. Preprint, submitted July 2, https://arxiv.org/abs/1007.0424.Google Scholar
  • [41] Pass B (2012) Multi-marginal optimal transport and multi-agent matching problems: Uniqueness and structure of solutions. Preprint, submitted October 27, https://arxiv.org/abs/1210.7372.Google Scholar
  • [42] Pass B (2015) Multi-marginal optimal transport: Theory and applications. ESAIM Math. Model. Numer. Anal. 49(6):1771–1790.CrossrefGoogle Scholar
  • [43] Peyré G, Cuturi M (2018) Computational optimal transport. Preprint, submitted March 1, https://arxiv.org/abs/1803.00567.Google Scholar
  • [44] Puccetti G, Rüschendorf L (2012) Bounds for joint portfolios of dependent risks. Statist. Risk Model. 29(2):107–132.CrossrefGoogle Scholar
  • [45] Rachev ST, Rüschendorf L (1998) Mass Transportation Problems: Volume 1: Theory (Springer Science & Business Media, New York).Google Scholar
  • [46] Ridder G, Moffitt R (2007) Chapter 75 the econometrics of data combination. Heckman JJ, Leamer EE, eds. Handbook of Econometrics, vol. 6, part B (Elsevier, Amsterdam), 5469–5547.CrossrefGoogle Scholar
  • [47] Rüschendorf L (1982) Random variables with maximum sums. Adv. Appl. Probab. 14(3):623–632.CrossrefGoogle Scholar
  • [48] Rüschendorf L (1991) Bounds for distributions with multivariate marginals. Mosler K, Scarsini M, eds. Stochastic Orders and Decision under Risk, IMS Lecture Notes Monograph Series, vol. 19 (Institute of Mathematical Statistics, Muenster, Germany), 285–310.CrossrefGoogle Scholar
  • [49] Santambrogio F (2015) Optimal Transport for Applied Mathematicians (Springer International Publishing, Cham, Switzerland).CrossrefGoogle Scholar
  • [50] Shortt RM (1983) Combinatorial methods in the study of marginal problems over separable spaces. J. Math. Anal. Appl. 97(2):462–479.CrossrefGoogle Scholar
  • [51] Sinha A, Namkoong H, Volpi R, Duchi J (2017) Certifying some distributional robustness with principled adversarial training. Preprint, submitted October 29, https://arxiv.org/abs/1710.10571.Google Scholar
  • [52] Villani C (2009) Optimal Transport: Old and New (Springer, Berlin).CrossrefGoogle Scholar
  • [53] Villani C (2021) Topics in Optimal Transportation (American Mathematical Society, Providence, RI).Google Scholar
  • [54] von Lindheim J (2022) Approximative algorithms for multi-marginal optimal transport and free-support Wasserstein Barycenters. Preprint, submitted February 2, https://arxiv.org/abs/2202.00954.Google Scholar
  • [55] Vorob’ev NN (1962) Consistent families of measures and their extensions. Theory Probab. Appl. 7(2):147–163.CrossrefGoogle Scholar
  • [56] Yue MC, Kuhn D, Wiesemann W (2022) On linear optimization over Wasserstein balls. Math. Programming 195(1–2):1107–1122.CrossrefGoogle Scholar
  • [57] Zhang L, Yang J, Gao R (2022) A simple duality proof for Wasserstein distributionally robust optimization. Preprint, submitted April 30, https://arxiv.org/abs/2205.00362.Google Scholar
  • [58] Zhao YQ, Zeng D, Tangen CM, Leblanc ML (2019) Robustifying trial-derived optimal treatment rules for a target population. Electronic J. Statist. 13(1):1717–1743.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.