Pairwise counter-monotonicity

We systematically study pairwise counter-monotonicity, an extremal notion of negative dependence. A stochastic representation and invariance property are established for this dependence structure. show that counter-monotonicity implies association, it is equivalent to joint mix if both possible the same marginal distributions. find intimate connection between risk sharing problems quantile agents. This result highlights importance structure in optimal allocations agents who not averse classic sense.