Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/227819
Authors: 
Nendel, Max
Year of Publication: 
2019
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 623
Abstract: 
In this work, we discuss completeness for the lattice orders of first and second order stochastic dominance. The main results state that, both, first and second order stochastic dominance induce Dedekind super complete lattices, i.e. lattices in which every bounded nonempty subset has a countable subset with identical least upper bound and greatest lower bound. Moreover, we show that, if a suitably bounded set of probability measures is directed (e.g. a lattice), then the supremum and infimum w.r.t. first or second order stochastic dominance can be approximated by sequences in the weak topology or in the Wasserstein-1 topology, respectively. As a consequence, we are able to prove that a sublattice of probability measures is complete w.r.t. first order stochastic dominance or second order stochastic dominance and increasing convex order if and only if it is compact in the weak topology or in the Wasserstein-1 topology, respectively. This complements a set of characterizations of tightness and uniform integrability, which are discussed in a preliminary section.
Subjects: 
Stochastic dominance
complete lattice
tightness
uniform integrability
Wassersteindistance
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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