Pareto efficiency for the concave order and multivariate comonotonicity

Carlier, Guillaume; Dana, Rose-Anne; Galichon, Alfred

Carlier, Guillaume; Dana, Rose-Anne; Galichon, Alfred (2012), Pareto efficiency for the concave order and multivariate comonotonicity, Journal of Economic Theory, 147, 1, p. 207-229. 10.1016/j.jet.2011.11.011

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Type

Article accepté pour publication ou publié

Date

2012

Journal name

Journal of Economic Theory

Volume

147

Number

Publisher

Elsevier

Pages

207-229

Abstract (EN)

This paper studies eﬃcient risk-sharing rules for the concave dominance order. For a univariate risk, it follows from a comonotone dominance principle, due to Landsberger and Meilijson [28], that eﬃciencyis characterized by a comonotonicity condition. The goal of the paper is to generalize the comonotone dominance principle as well asthe equivalence between eﬃciency and comonotonicity to the multidimensional case. The multivariate case is more involved (in particularbecause there is no immediate extension of the notion of comonotonicity) and it is addressed by using techniques from convex duality andoptimal transportation.

Subjects / Keywords

stochastic dominance; Efficiency; Comonotonicity; Concave order; Stochastic dominance; Multivariate risk-sharing

JEL

D81 - Criteria for Decision-Making under Risk and Uncertainty
D61 - Allocative Efficiency; Cost–Benefit Analysis
C61 - Optimization Techniques; Programming Models; Dynamic Analysis