Multidimensional inequalities and generalized quantile functions

Sinem Bas (1) , Philippe Bich (2, 3) , Alain Chateauneuf (2, 3)

1 UCL - Université Catholique de Louvain = Catholic University of Louvain
2 CES - Centre d'économie de la Sorbonne
3 PSE - Paris School of Economics

In this paper, we extend the generalized Yaari dual theory for multidimen-sional distributions, in the vein of Galichon and Henry's paper [6]. We show how a class of generalized quantiles-which encompasses Galichon and Henry's one or multivariate quantile transform [7] [4] [9]-allows to derive a general representation theorem. Moreover, we derive from this representation theorem a formula which could be applicable to multidimensional measure of inequality.

Mots clés: multidimensional distributions; quantile; inequality; optimal coupling

Domaines: Economies et finances

Sinem Bas, Philippe Bich, Alain Chateauneuf. Multidimensional inequalities and generalized quantile functions. 2016. ⟨hal-01313118⟩