  This article proposes a generalized notion of extreme multivariate dependence
between two random vectors which relies on the extremality of the
cross-covariance matrix between these two vectors. Using a partial ordering on
the cross-covariance matrices, we also generalize the notion of positive upper
dependence. We then proposes a means to quantify the strength of the dependence
between two given multivariate series and to increase this strength while
preserving the marginal distributions. This allows for the design of
stress-tests of the dependence between two sets of financial variables, that
can be useful in portfolio management or derivatives pricing.
