# Stochastic order relations and lattices of probability measures

Abstract : 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.
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Journal articles

https://hal-hec.archives-ouvertes.fr/hal-00539119
Contributor : Antoine Haldemann <>
Submitted on : Wednesday, November 24, 2010 - 9:48:07 AM
Last modification on : Thursday, January 11, 2018 - 6:19:31 AM

### Citation

Marco Scarsini, Alfred Muller. Stochastic order relations and lattices of probability measures. SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2006, Vol.16, N°4, pp.1024 - 1043. ⟨10.1137/040611021⟩. ⟨hal-00539119⟩

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