  Set-valued quantiles for multivariate distributions with respect to a general
convex cone are introduced which are based on a family of (univariate)
distribution functions rather than on the joint distribution function. It is
shown that these quantiles enjoy basically all the properties of univariate
quantile functions. Relationships to families of univariate quantile functions
and to depth functions are discussed. Finally, a corresponding Value at Risk
for multivariate random variables as well as stochastic orders are introduced
via the set-valued approach.
