  We propose a multivariate extension of a well-known characterization by S.
Kusuoka of regular and coherent risk measures as maximal correlation
functionals. This involves an extension of the notion of comonotonicity to
random vectors through generalized quantile functions. Moreover, we propose to
replace the current law invariance, subadditivity and comonotonicity axioms by
an equivalent property we call strong coherence and that we argue has more
natural economic interpretation. Finally, we reformulate the computation of
regular and coherent risk measures as an optimal transportation problem, for
which we provide an algorithm and implementation.
