https://hec.hal.science/hal-00540198Scarsini, MarcoMarcoScarsiniGREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche ScientifiqueDipartimento di Scienze Economiche e Aziendali - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma]Muller, AlfredAlfredMullerStochastic comparison of random vectors with a common copulaHAL CCSD2001Directionally convex orderlocal mean preserving spreadcopulaconditionally increasing random vectorsconvex orderingportfolio optimization[SHS.ECO.ECO] Humanities and Social Sciences/Economics and Finance/Economy and decision scienceHaldemann, Antoine2010-11-26 10:00:262023-03-24 14:52:532010-11-26 10:00:26enJournal articles10.1287/moor.26.4.723.100061We consider two random vectors X and Y, such that the components of X are dominated in the convex order by the corresponding components of Y. We want to find conditions under which this implies that any positive linear combination of the components of X is dominated in the convex order by the same positive linear combination of the components of Y. This problem has a motivation in the comparison of portfolios in terms of risk. The conditions for the above dominance will concern the dependence structure of the two random vectors X and Y, namely, the two random vectors will have a common copula and will be conditionally increasing. This new concept of dependence is strictly related to the idea of conditionally increasing in sequence, but, in addition, it is invariant under permutation. We will actually prove that, under the above conditions, X will be dominated by Y in the directionally convex order, which yields as a corollary the dominance for positive linear combinations. This result will be applied to a portfolio optimization problem.