A note on stochastic dominance, uniform integrability and lattice properties

Nendel M (2020)
Bulletin of the London Mathematical Society 52(5): 907-923.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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.
Stichworte
60E15 (primary); 60B10; 06B23 (secondary)
Erscheinungsjahr
2020
Zeitschriftentitel
Bulletin of the London Mathematical Society
Band
52
Ausgabe
5
Seite(n)
907-923
ISSN
0024-6093
eISSN
1469-2120
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
Page URI
https://pub.uni-bielefeld.de/record/2944509

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Nendel M. A note on stochastic dominance, uniform integrability and lattice properties. Bulletin of the London Mathematical Society. 2020;52(5):907-923.
Nendel, M. (2020). A note on stochastic dominance, uniform integrability and lattice properties. Bulletin of the London Mathematical Society, 52(5), 907-923. https://doi.org/10.1112/blms.12371
Nendel, M. (2020). A note on stochastic dominance, uniform integrability and lattice properties. Bulletin of the London Mathematical Society 52, 907-923.
Nendel, M., 2020. A note on stochastic dominance, uniform integrability and lattice properties. Bulletin of the London Mathematical Society, 52(5), p 907-923.
M. Nendel, “A note on stochastic dominance, uniform integrability and lattice properties”, Bulletin of the London Mathematical Society, vol. 52, 2020, pp. 907-923.
Nendel, M.: A note on stochastic dominance, uniform integrability and lattice properties. Bulletin of the London Mathematical Society. 52, 907-923 (2020).
Nendel, Max. “A note on stochastic dominance, uniform integrability and lattice properties”. Bulletin of the London Mathematical Society 52.5 (2020): 907-923.
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2021-01-29T12:37:56Z
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