Stochastic Ordering of Bivariate Elliptical Distributions

Abstract

It is shown that for elliptically distributed bivariate random vectors, the riskiness and dependence strength of random portfolios, in the sense of the univariate convex and bivariate concordance stochastic orders respectively, can be simply characterised in terms of the vector's $\mathbf{\Sigma}$-matrix.

Keywords: Elliptical distributions, convex order, concordance order, dependence, risk management