%0 Journal Article
%T Stochastic order relations and lattices of probability measures
%+ Groupement de Recherche et d'Etudes en Gestion à HEC (GREGH)
%+ Dipartimento di Scienze Economiche e Aziendali
%A Scarsini, Marco
%A Muller, Alfred
%< avec comité de lecture
%@ 1052-6234
%J SIAM Journal on Optimization
%I Society for Industrial and Applied Mathematics
%V Vol.16, N°4
%P pp.1024 - 1043
%8 2006
%D 2006
%R 10.1137/040611021
%K copula
%K zonoid
%K lattice
%K univariate stochastic orders
%K multivariate stochastic orders
%K optimization with stochastic dominance constraints
%Z Humanities and Social Sciences/Economics and Finance/domain_shs.eco.ecoJournal articles
%X We 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.
%G English
%L hal-00539119
%U https://hec.hal.science/hal-00539119
%~ SHS
%~ HEC
%~ CNRS
%~ AO-ECONOMIE