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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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    1. Chambers, Christopher P., 2007. "Ordinal aggregation and quantiles," Journal of Economic Theory, Elsevier, vol. 137(1), pages 416-431, November.
    2. Manski, Charles F., 1986. "Ordinal Utility Models Of Decision Making Under Uncertainty," SSRI Workshop Series 292682, University of Wisconsin-Madison, Social Systems Research Institute.
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    4. Kevin W. S. Roberts, 1980. "Possibility Theorems with Interpersonally Comparable Welfare Levels," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(2), pages 409-420.
    5. Gevers, Louis, 1979. "On Interpersonal Comparability and Social Welfare Orderings," Econometrica, Econometric Society, vol. 47(1), pages 75-89, January.
    6. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 173-183, November.
    7. Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
    8. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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