TY - JOUR
T1 - Dual theory of choice with multivariate risks
AU - Galichon, Alfred
AU - Henry, Marc
N1 - 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 Société Générale “Risques Financiers”. Galichon’s research is partly supported by the Chaire EDF-Calyon “Finance and Développement Durable” and FiME, Laboratoire de Finance des Marchés de l’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: [email protected] (A. Galichon), [email protected] (M. Henry).
PY - 2012/7
Y1 - 2012/7
N2 - 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.
AB - 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.
KW - Gini evaluation functions
KW - Multi-attribute inequality
KW - Multivariate comonotonicity
KW - Optimal transportation
KW - Rank dependent utility theory
KW - Risk
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U2 - 10.1016/j.jet.2011.06.002
DO - 10.1016/j.jet.2011.06.002
M3 - Article
AN - SCOPUS:84155165897
SN - 0022-0531
VL - 147
SP - 1501
EP - 1516
JO - Journal of Economic Theory
JF - Journal of Economic Theory
IS - 4
ER -