Hessian and increasing-Hessian orderings of multivariate skew-elliptical random vectors

In this work, we establish some stochastic comparison results for multivariate skew-elliptical random vectors. These multivariate stochastic comparisons involve Hessian and increasing-Hessian orderings as well as many of their special cases. Necessary and/or sufficient conditions of the orderings are provided simply based on a comparison of the underlying model parameters.