TY  - GEN
AB  - 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.
DA  - 2019
KW  - Stochastic dominance
KW  - complete lattice
KW  - tightness
KW  - uniform integrability
KW  - Wasserstein distance
LA  - eng
PY  - 2019
SN  - 0931-6558
SP  - 17-
TI  - A Note on Stochastic Dominance and Compactness
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29372610
Y2  - 2024-11-24T10:44:28
ER  -