Relationship between multivariate concordance and risk measures

The question about the definition of concordance between random vectors is an open problem because there is not an unanimous opinion about its meaning and its appropriate definition. Also the definition of multivariate risk measures encounters many difficulties. In this paper we want to investigate the relationship between these multivariate measures, essentially based on the relation between riskiness and association, and between joint and marginal distribution functions. We propose an axiomatic approach based on a minimal set of properties and we give a characterization of some particular classes of multivariate and bivariate risk measures. In the end we introduce new kinds of measures: the multivariate distorted risk measures and a product stop-loss premium for random vectors.