https://hec.hal.science/hal-00539119Scarsini, 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 order relations and lattices of probability measuresHAL CCSD2006copulazonoidlatticeunivariate stochastic ordersmultivariate stochastic ordersoptimization with stochastic dominance constraints[SHS.ECO.ECO] Humanities and Social Sciences/Economics and Finance/Economy and decision scienceHaldemann, Antoine2010-11-24 09:48:072023-03-24 14:52:532010-11-24 09:48:07enJournal articles10.1137/0406110211We study various partially ordered spaces of probability measures and we determine which of them are lattices. This has important consequences for optimization problems with stochastic dominance constraints. In particular we show that the space of probability measures on $\mathbb{R}$ is a lattice under most of the known partial orders, whereas the space of probability measures on $\mathbb{R}^d$ typically is not. Nevertheless, some subsets of this space, defined by imposing strong conditions on the dependence structure of the measures, are lattices.