https://hal-hec.archives-ouvertes.fr/hal-00491679Scarsini, MarcoMarcoScarsiniGREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche ScientifiqueArlotto, AlexandroAlexandroArlottoOPIM Department - University of Pennsylvania [Philadelphia]Hessian orders and multinormal distributionsHAL CCSD2009Hessian ordersMultivariate normal distributionConvex conesDual spaceCompletely positive order[SHS.ECO.ECO] Humanities and Social Sciences/Economics and Finance/Economy and decision scienceHaldemann, Antoine2010-06-14 10:17:582022-06-25 10:50:522010-06-14 14:03:44enJournal articles10.1016/j.jmva.2009.03.0091Several 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, i.e., an integral stochastic order defined through a convex cone of Hessian matrices, 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.