Equivalent or absolutely continuous probability measures with given marginals

Berti Patrizia, Pratelli Luca, Rigo Pietro and Spizzichino Fabio
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Berti Patrizia: Dipartimento di Matematica Pura ed Applicata ”G. Vitali”, Universita’ di Modena e Reggio-Emilia, via Campi 213/B, 41100 Modena, Italy
Pratelli Luca: Accademia Navale, viale Italia 72, 57100 Livorno, Italy
Rigo Pietro: Dipartimento di Matematica ”F. Casorati”, Universita’ di Pavia, via Ferrata 1, 27100 Pavia, Italy
Spizzichino Fabio: Dipartimento di Matematica ”G. Castelnuovo”, Universita’ di Roma ”La Sapienza”, piazzale A. Moro 5, 00185 Roma, Italy

Dependence Modeling, 2015, vol. 3, issue 1, 12

Abstract: Let (X,A) and (Y,B) be measurable spaces. Supposewe are given a probability α on A, a probability β on B and a probability μ on the product σ-field A ⊗ B. Is there a probability ν on A⊗B, with marginals α and β, such that ν ≪ μ or ν ~ μ ? Such a ν, provided it exists, may be useful with regard to equivalent martingale measures and mass transportation. Various conditions for the existence of ν are provided, distinguishing ν ≪ μ from ν ~ μ.

Keywords: Coupling; Domination on rectangles; Equivalent martingale measure; Finitely additive probability measure; Mass transportat; 60A05; 60A10; 28A35; Coupling; Domination on rectangles; Equivalent martingale measure; Finitely additive probability measure; Mass transportat; 60A05; 60A10; 28A35 (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:3:y:2015:i:1:p:12:n:4

DOI: 10.1515/demo-2015-0004

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