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An Axiomatization Of Quantiles On The Domain Of Distribution Functions

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  • Christopher P. Chambers

Abstract

In an environment in which the primitive is the space of distribution functions, we characterize the quantile functions by the axioms ordinal covariance, monotonicity with respect to first‐order stochastic dominance, and upper semicontinuity. We show how to characterize the VaR in a similar manner.

Suggested Citation

  • Christopher P. Chambers, 2009. "An Axiomatization Of Quantiles On The Domain Of Distribution Functions," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 335-342, April.
    • Handle: RePEc:bla:mathfi:v:19:y:2009:i:2:p:335-342
    DOI: 10.1111/j.1467-9965.2009.00369.x
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    References listed on IDEAS

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    Cited by:

    1. Castro, Luciano de & Galvao, Antonio F. & Kim, Jeong Yeol & Montes-Rojas, Gabriel & Olmo, Jose, 2022. "Experiments on portfolio selection: A comparison between quantile preferences and expected utility decision models," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 97(C).
    2. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2014. "Beyond cash-additive risk measures: when changing the numéraire fails," Finance and Stochastics, Springer, vol. 18(1), pages 145-173, January.
    3. Xia Han & Bin Wang & Ruodu Wang & Qinyu Wu, 2021. "Risk Concentration and the Mean-Expected Shortfall Criterion," Papers 2108.05066, arXiv.org, revised Apr 2022.
    4. Ceriani,Lidia & Verme,Paolo, 2018. "Risk preferences and the decision to flee conflict," Policy Research Working Paper Series 8376, The World Bank.
    5. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    6. de Castro, Luciano & Galvao, Antonio F. & Noussair, Charles N. & Qiao, Liang, 2022. "Do people maximize quantiles?," Games and Economic Behavior, Elsevier, vol. 132(C), pages 22-40.
    7. Mikhail Sokolov, 2011. "Interval scalability of rank-dependent utility," Theory and Decision, Springer, vol. 70(3), pages 255-282, March.
    8. Xue Dong He & Zhaoli Jiang & Steven Kou, 2020. "Portfolio Selection under Median and Quantile Maximization," Papers 2008.10257, arXiv.org, revised Mar 2021.
    9. Fabio Bellini & Ilaria Peri, 2021. "An axiomatization of $\Lambda$-quantiles," Papers 2109.02360, arXiv.org, revised Jan 2022.
    10. Long, Yan & Sethuraman, Jay & Xue, Jingyi, 2021. "Equal-quantile rules in resource allocation with uncertain needs," Journal of Economic Theory, Elsevier, vol. 197(C).
    11. Luciano de Castro & Antonio F. Galvao & Gabriel Montes-Rojas & Jose Olmo, 2022. "Portfolio selection in quantile decision models," Annals of Finance, Springer, vol. 18(2), pages 133-181, June.
    12. Xia Han & Qiuqi Wang & Ruodu Wang & Jianming Xia, 2021. "Cash-subadditive risk measures without quasi-convexity," Papers 2110.12198, arXiv.org, revised Mar 2022.
    13. Hirbod Assa & Liyuan Lin & Ruodu Wang, 2022. "Calibrating distribution models from PELVE," Papers 2204.08882, arXiv.org, revised Jun 2023.
    14. Jarrod Burgh & Emerson Melo, 2023. "Wishful Thinking is Risky Thinking," Papers 2307.02422, arXiv.org, revised Feb 2024.
    15. Gribkova, N.V. & Su, J. & Zitikis, R., 2022. "Inference for the tail conditional allocation: Large sample properties, insurance risk assessment, and compound sums of concomitants," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 199-222.
    16. Xue Dong He & Zhaoli Jiang, 2020. "Optimal Payoff under the Generalized Dual Theory of Choice," Papers 2012.00345, arXiv.org.
    17. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    18. de Castro, Luciano & Galvao, Antonio F. & Muchon, Andre, 2023. "Numerical Solution of Dynamic Quantile Models," Journal of Economic Dynamics and Control, Elsevier, vol. 148(C).
    19. Ruodu Wang & Ričardas Zitikis, 2021. "An Axiomatic Foundation for the Expected Shortfall," Management Science, INFORMS, vol. 67(3), pages 1413-1429, March.
    20. de Castro, Luciano & Galvao, Antonio F. & Montes-Rojas, Gabriel, 2020. "Quantile selection in non-linear GMM quantile models," Economics Letters, Elsevier, vol. 195(C).
    21. Luciano Castro & Antonio F. Galvao, 2022. "Static and dynamic quantile preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 747-779, April.

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