@article{3d984efb1c144bc8b53c3e0297dab327,
title = "Dual theory of choice with multivariate risks",
abstract = "We propose a multivariate extension of Yaari's dual theory of choice under risk. We show that a decision maker with a preference relation on multidimensional prospects that preserves first order stochastic dominance and satisfies comonotonic independence behaves as if evaluating prospects using a weighted sum of quantiles. Both the notions of quantiles and of comonotonicity are extended to the multivariate framework using optimal transportation maps. Finally, risk averse decision makers are characterized within this framework and their local utility functions are derived. Applications to the measurement of multi-attribute inequality are also discussed.",
keywords = "Gini evaluation functions, Multi-attribute inequality, Multivariate comonotonicity, Optimal transportation, Rank dependent utility theory, Risk",
author = "Alfred Galichon and Marc Henry",
note = "Funding Information: Keywords: Risk; Rank dependent utility theory; Multivariate comonotonicity; Optimal transportation; Multi-attribute inequality; Gini evaluation functions ✩ Both authors gratefully acknowledge support from the Chaire Axa “Assurance des Risques Majeurs” and the Chaire Soci{\'e}t{\'e} G{\'e}n{\'e}rale “Risques Financiers”. Galichon{\textquoteright}s research is partly supported by the Chaire EDF-Calyon “Finance and D{\'e}veloppement Durable” and FiME, Laboratoire de Finance des March{\'e}s de l{\textquoteright}Energie (http://www.fime-lab.org). The authors thank Thibault Gajdos, John Weymark and the participants at the 2010 ParisTech–Journal of Economic Theory Symposium on Inequality and Risk for helpful discussions and comments. The authors are grateful to two anonymous referees and particularly an Associate Editor for their careful reading of the manuscript and insightful suggestions. * Corresponding authors. E-mail addresses: alfred.galichon@polytechnique.edu (A. Galichon), marc.henry@umontreal.ca (M. Henry).",
year = "2012",
month = jul,
doi = "10.1016/j.jet.2011.06.002",
language = "English (US)",
volume = "147",
pages = "1501--1516",
journal = "Journal of Economic Theory",
issn = "0022-0531",
publisher = "Academic Press Inc.",
number = "4",
}