Pareto efficiency for the concave order and multivariate comonotonicity

Details Pareto efficiency for the concave order and multivariate comonotonicity Pareto efficiency for the concave order and multivariate comonotonicity

2009-12-02

arxiv.org/abs/0912.0509v2

Mathematics

Optimization and Control

Scientific paper

In this paper, we focus on 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 [25], that efficiency is characterized by a comonotonicity condition. The goal of this paper is to generalize the comonotone dominance principle as well as the equivalence between efficiency and comonotonicity to the multi-dimensional case. The multivariate setting is more involved (in particular because there is no immediate extension of the notion of comonotonicity) and we address it using techniques from convex duality and optimal transportation.

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