%0 Journal Article %T Hessian orders and multinormal distributions - à paraître %+ Groupement de Recherche et d'Etudes en Gestion à HEC (GREGH) %+ Dipartimento di Scienze Economiche e Aziendali %A Scarsini, Marco %A Arlotto, Alessandro %< avec comité de lecture %@ 0047-259X %J Journal of Multivariate Analysis %I Elsevier %V Vol. 100 %P pp. 2324-2330 %8 2009 %D 2009 %R 10.1016/j.jmva.2009.03.009 %K Hessian orders %K Multivariate normal distribution %K Convex cones %K Dual space %K Completely positive order %Z Humanities and Social Sciences/Economics and Finance/domain_shs.eco.ecoJournal articles %X Several well known integral stochastic orders (like the convex order, the supermodular order, etc.) can be defined in terms of the Hessian matrix of a class of functions. Here we consider a generic Hessian order and we prove that if two random vectors are ordered by the Hessian order, then their means are equal and the difference of their covariance matrices belongs to the dual of H. Then we show that the same conditions are also sufficient for multinormal random vectors. We study several particular cases of this general result. %G English %L hal-00542400 %U https://hec.hal.science/hal-00542400 %~ SHS %~ HEC %~ CNRS %~ AO-ECONOMIE