TY  - JOUR
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, that is, 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 (for example, a lattice), then the supremum and infimum with respect to first-order 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 with respect to 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  - 2020
DO  - 10.1112/blms.12371
KW  - 60E15 (primary)
KW  - 60B10
KW  - 06B23 (secondary)
LA  - eng
IS  - 5
M2  - 907
PY  - 2020
SN  - 0024-6093
SP  - 907-923
T2  - Bulletin of the London Mathematical Society
TI  - A note on stochastic dominance, uniform integrability and lattice properties
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29445099
Y2  - 2024-11-22T05:19:45
ER  -