IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v73y2025i2p879-893.html

Multivariate Almost Stochastic Dominance: Transfer Characterizations and Sufficient Conditions Under Dependence Uncertainty

Author

Listed:
  • Alfred Müller

    (Department Mathematik, Universität Siegen, 57072 Siegen, Germany)

  • Marco Scarsini

    (Dipartimento di Economia e Finanza, Luiss University, 00197 Roma, Italy)

  • Ilia Tsetlin

    (INSEAD, Singapore 138676)

  • Robert L. Winkler

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

Abstract

Most often, important decisions involve several unknown attributes. This produces a double challenge in the sense that both assessing the individual multiattribute preferences and assessing the joint distribution of the attributes can be extremely hard. To handle the first challenge, we suggest multivariate almost stochastic dominance, a relation based on bounding marginal utilities. We provide necessary and sufficient characterizations in terms of simple transfers, which are easily communicated to decision makers and, thus, can be used for preference elicitation. To handle the second challenge, we develop sufficient conditions that do not consider the dependence structure and are based on either marginal distributions of the attributes or just their means and variances. We apply the theoretical results to a case study of comparing the efficiency of photovoltaic plants.

Suggested Citation

  • Alfred Müller & Marco Scarsini & Ilia Tsetlin & Robert L. Winkler, 2025. "Multivariate Almost Stochastic Dominance: Transfer Characterizations and Sufficient Conditions Under Dependence Uncertainty," Operations Research, INFORMS, vol. 73(2), pages 879-893, March.
    • Handle: RePEc:inm:oropre:v:73:y:2025:i:2:p:879-893
    DOI: 10.1287/opre.2022.0596
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2022.0596
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2022.0596?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Ilia Tsetlin & Robert L. Winkler, 2005. "Risky Choices and Correlated Background Risk," Management Science, INFORMS, vol. 51(9), pages 1336-1345, September.
    2. Li, Y.Z. & Wu, Q.H. & Li, M.S. & Zhan, J.P., 2014. "Mean-variance model for power system economic dispatch with wind power integrated," Energy, Elsevier, vol. 72(C), pages 510-520.
    3. Michel Denuit & Rachel Huang & Larry Tzeng, 2014. "Bivariate almost stochastic dominance," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(2), pages 377-405, October.
    4. George L. O'Brien & Marco Scarsini, 1991. "Multivariate Stochastic Dominance and Moments," Mathematics of Operations Research, INFORMS, vol. 16(2), pages 382-389, May.
    5. Marco Scarsini, 1988. "Dominance Conditions for Multivariate Utility Functions," Management Science, INFORMS, vol. 34(4), pages 454-460, April.
    6. François Baccelli & Armand M. Makowski, 1989. "Multidimensional Stochastic Ordering and Associated Random Variables," Operations Research, INFORMS, vol. 37(3), pages 478-487, June.
    7. Carole Bernard & Michel Denuit & Steven Vanduffel, 2018. "Measuring Portfolio Risk Under Partial Dependence Information," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(3), pages 843-863, September.
    8. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel, 2017. "Value-at-Risk Bounds With Variance Constraints," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 923-959, September.
    9. David Ardia & Keven Bluteau & Kris Boudt & Koen Inghelbrecht, 2023. "Climate Change Concerns and the Performance of Green vs. Brown Stocks," Management Science, INFORMS, vol. 69(12), pages 7607-7632, December.
    10. Paul Embrechts & Bin Wang & Ruodu Wang, 2015. "Aggregation-robustness and model uncertainty of regulatory risk measures," Finance and Stochastics, Springer, vol. 19(4), pages 763-790, October.
    11. Larry Y. Tzeng & Rachel J. Huang & Pai-Ta Shih, 2013. "Revisiting Almost Second-Degree Stochastic Dominance," Management Science, INFORMS, vol. 59(5), pages 1250-1254, May.
    12. Ilia Tsetlin & Robert L. Winkler & Rachel J. Huang & Larry Y. Tzeng, 2015. "Generalized Almost Stochastic Dominance," Operations Research, INFORMS, vol. 63(2), pages 363-377, April.
    13. Mario Ghossoub & Jesse Hall & David Saunders, 2023. "Maximum Spectral Measures of Risk with Given Risk Factor Marginal Distributions," Mathematics of Operations Research, INFORMS, vol. 48(2), pages 1158-1182, May.
    14. Müller, Alfred & Reuber, Matthias, 2023. "A copula-based time series model for global horizontal irradiation," International Journal of Forecasting, Elsevier, vol. 39(2), pages 869-883.
    15. Østerdal, Lars Peter, 2010. "The mass transfer approach to multivariate discrete first order stochastic dominance: Direct proof and implications," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1222-1228, November.
    16. Kwon, Soon-Duck, 2010. "Uncertainty analysis of wind energy potential assessment," Applied Energy, Elsevier, vol. 87(3), pages 856-865, March.
    17. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
    18. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    19. Bernard, Carole & Jiang, Xiao & Wang, Ruodu, 2014. "Risk aggregation with dependence uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 93-108.
    20. Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
    21. Shushang Zhu & Masao Fukushima, 2009. "Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management," Operations Research, INFORMS, vol. 57(5), pages 1155-1168, October.
    22. Azlan, F. & Kurnia, J.C. & Tan, B.T. & Ismadi, M.-Z., 2021. "Review on optimisation methods of wind farm array under three classical wind condition problems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 135(C).
    23. David Levhari & Jacob Paroush & Bezalel Peleg, 1975. "Efficiency Analysis for Multivariate Distributions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(1), pages 87-91.
    24. Alfred Müller & Marco Scarsini & Ilia Tsetlin & Robert L. Winkler, 2022. "Technical Note—Ranking Distributions When Only Means and Variances Are Known," Operations Research, INFORMS, vol. 70(5), pages 2851-2859, September.
    25. Mao, Tiantian & Wang, Ruodu, 2022. "Fractional stochastic dominance in rank-dependent utility and cumulative prospect theory," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    26. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    27. Peter C. Fishburn, 1980. "Stochastic Dominance and Moments of Distributions," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 94-100, February.
    28. Vinit Kumar Mishra & Karthik Natarajan & Dhanesh Padmanabhan & Chung-Piaw Teo & Xiaobo Li, 2014. "On Theoretical and Empirical Aspects of Marginal Distribution Choice Models," Management Science, INFORMS, vol. 60(6), pages 1511-1531, June.
    29. Rachel J. Huang & Larry Y. Tzeng & Lin Zhao, 2020. "Fractional Degree Stochastic Dominance," Management Science, INFORMS, vol. 66(10), pages 4630-4647, October.
    30. Xuan Vinh Doan & Karthik Natarajan, 2012. "On the Complexity of Nonoverlapping Multivariate Marginal Bounds for Probabilistic Combinatorial Optimization Problems," Operations Research, INFORMS, vol. 60(1), pages 138-149, February.
    31. Müller, Alfred & Scarsini, Marco, 2012. "Fear of loss, inframodularity, and transfers," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1490-1500.
    32. Karthik Natarajan & Miao Song & Chung-Piaw Teo, 2009. "Persistency Model and Its Applications in Choice Modeling," Management Science, INFORMS, vol. 55(3), pages 453-469, March.
    33. Xuan Vinh Doan & Xiaobo Li & Karthik Natarajan, 2015. "Robustness to Dependency in Portfolio Optimization Using Overlapping Marginals," Operations Research, INFORMS, vol. 63(6), pages 1468-1488, December.
    34. Pratt, John W, 1988. "Aversion to One Risk in the Presence of Others," Journal of Risk and Uncertainty, Springer, vol. 1(4), pages 395-413, December.
    35. Levy, Haim & Paroush, Jacob, 1974. "Toward multivariate efficiency criteria," Journal of Economic Theory, Elsevier, vol. 7(2), pages 129-142, February.
    36. Louis Chen & Will Ma & Karthik Natarajan & David Simchi-Levi & Zhenzhen Yan, 2022. "Distributionally Robust Linear and Discrete Optimization with Marginals," Operations Research, INFORMS, vol. 70(3), pages 1822-1834, May.
    37. Stelios Arvanitis & Thierry Post & Nikolas Topaloglou, 2021. "Stochastic Bounds for Reference Sets in Portfolio Analysis," Management Science, INFORMS, vol. 67(12), pages 7737-7754, December.
    38. Ilia Tsetlin & Robert L. Winkler, 2018. "Multivariate Almost Stochastic Dominance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(2), pages 431-445, June.
    39. K. C. Mosler, 1984. "Stochastic Dominance Decision Rules when the Attributes are Utility Independent," Management Science, INFORMS, vol. 30(11), pages 1311-1322, November.
    40. Alfred Müller & Marco Scarsini & Ilia Tsetlin & Robert L. Winkler, 2017. "Between First- and Second-Order Stochastic Dominance," Management Science, INFORMS, vol. 63(9), pages 2933-2947, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chen, An & Müller, Alfred & Rach, Manuel, 2025. "The tontine puzzle," Journal of Mathematical Economics, Elsevier, vol. 121(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jose Blanchet & Henry Lam & Yang Liu & Ruodu Wang, 2025. "Convolution Bounds on Quantile Aggregation," Operations Research, INFORMS, vol. 73(5), pages 2761-2781, September.
    2. Chunling Luo & Piao Chen & Patrick Jaillet, 2025. "Portfolio Optimization Based on Almost Second-Degree Stochastic Dominance," Management Science, INFORMS, vol. 71(8), pages 7029-7055, August.
    3. Yichun Chi & Zuo Quan Xu & Sheng Chao Zhuang, 2022. "Distributionally Robust Goal-Reaching Optimization in the Presence of Background Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 26(3), pages 351-382, August.
    4. Christian Laudag'e & Felix-Benedikt Liebrich, 2025. "When risk defies order: On the limits of fractional stochastic dominance," Papers 2509.24747, arXiv.org.
    5. Wang, Hongxia & Zhou, Lin & Dai, Peng-Fei & Xiong, Xiong, 2022. "Moment conditions for fractional degree stochastic dominance," Finance Research Letters, Elsevier, vol. 49(C).
    6. Østerdal, Lars Peter, 2010. "The mass transfer approach to multivariate discrete first order stochastic dominance: Direct proof and implications," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1222-1228, November.
    7. Zhao, Kena & Ng, Tsan Sheng & Tan, Chin Hon & Pang, Chee Khiang, 2021. "An almost robust model for minimizing disruption exposures in supply systems," European Journal of Operational Research, Elsevier, vol. 295(2), pages 547-559.
    8. Chun Peng & Erick Delage, 2024. "Data-Driven Optimization with Distributionally Robust Second Order Stochastic Dominance Constraints," Operations Research, INFORMS, vol. 72(3), pages 1298-1316, May.
    9. Francesco Cesarone & Justo Puerto, 2024. "New approximate stochastic dominance approaches for Enhanced Indexation models," Papers 2401.12669, arXiv.org.
    10. Louis Chen & Will Ma & Karthik Natarajan & David Simchi-Levi & Zhenzhen Yan, 2022. "Distributionally Robust Linear and Discrete Optimization with Marginals," Operations Research, INFORMS, vol. 70(3), pages 1822-1834, May.
    11. Liu, Liqun & Meyer, Jack, 2025. "Almost stochastic dominance: Magnitude constraints on risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 122(C), pages 82-90.
    12. Argyris, Nikolaos & Østerdal, Lars Peter & Hussain, M. Azhar, 2025. "Value-driven multidimensional welfare analysis: A dominance approach with application to comparisons of European populations," European Journal of Operational Research, Elsevier, vol. 324(1), pages 200-220.
    13. Cesarone, Francesco & Puerto, Justo, 2025. "Flexible enhanced indexation models through stochastic dominance and ordered weighted average optimization," European Journal of Operational Research, Elsevier, vol. 323(2), pages 657-670.
    14. Viet Anh Nguyen & Soroosh Shafiee & Damir Filipovi'c & Daniel Kuhn, 2021. "Mean-Covariance Robust Risk Measurement," Papers 2112.09959, arXiv.org, revised Oct 2025.
    15. Silvana Pesenti & Qiuqi Wang & Ruodu Wang, 2020. "Optimizing distortion riskmetrics with distributional uncertainty," Papers 2011.04889, arXiv.org, revised Feb 2022.
    16. Henry Chiu, W., 2020. "Financial risk taking in the presence of correlated non-financial background risk," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 167-179.
    17. Mengshi Lu & Zuo‐Jun Max Shen, 2021. "A Review of Robust Operations Management under Model Uncertainty," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1927-1943, June.
    18. Frank A Cowell & Martyna Kobus & Radoslaw Kurek, 2017. "Welfare and Inequality Comparisons for Uni- and Multi-dimensional Distributions of Ordinal Data," STICERD - Public Economics Programme Discussion Papers 31, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    19. Haiyan Liu & Bin Wang & Ruodu Wang & Sheng Chao Zhuang, 2023. "Distorted optimal transport," Papers 2308.11238, arXiv.org, revised May 2025.
    20. Rüschendorf, L., 2019. "Analysis of risk bounds in partially specified additive factor models," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 115-121.

    More about this item

    Keywords

    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:73:y:2025:i:2:p:879-893. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.