Dual theory of choice under multivariate risks

Alfred Galichon (1) , Marc Henry (2)

1 ECON - Département d'économie (Sciences Po)
2 Départment de sciences économiques

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 ¯rst order stochastic dominance and satis¯es comonotonic in-dependence behaves as if evaluating prospects with 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, and we show how to efficiently compute the functionals they use to evaluate prospects.

Keywords: Risk; Rank dependent utility theory; Multivariate comonotonicity; Optimal transportation; Multi-attribute inequality; Gini evaluation functions

Domains: Economics and Finance

Alfred Galichon, Marc Henry. Dual theory of choice under multivariate risks. Journal of Economic Theory, 2012, 147 (4), pp.1501-1516. ⟨10.1016/j.jet.2011.06.002⟩. ⟨hal-01024582⟩