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AN AXIOMATIZATION OF QUANTILES ON THE DOMAIN OF DISTRIBUTION FUNCTIONS
Author(s) -
Chambers Christopher P.
Publication year - 2009
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2009.00369.x
Subject(s) - quantile , mathematics , stochastic dominance , monotonic function , covariance , stochastic ordering , quantile function , distribution (mathematics) , econometrics , axiom , statistics , probability distribution , mathematical analysis , moment generating function , geometry
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.