Equivalent or absolutely continuous probability measures with given marginals
Patrizia Berti; Luca Pratelli; Pietro Rigo; Fabio Spizzichino
Dependence Modeling (2015)
- Volume: 3, Issue: 1, page 47-58, electronic only
- ISSN: 2300-2298
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topPatrizia Berti, et al. "Equivalent or absolutely continuous probability measures with given marginals." Dependence Modeling 3.1 (2015): 47-58, electronic only. <http://eudml.org/doc/270847>.
@article{PatriziaBerti2015,
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.},
author = {Patrizia Berti, Luca Pratelli, Pietro Rigo, Fabio Spizzichino},
journal = {Dependence Modeling},
keywords = {Coupling; Domination on rectangles; Equivalent martingale measure; Finitely additive probability
measure; Mass transportat; coupling; domination on rectangles; equivalent martingale measure; finitely additive probability measure; mass transportat},
language = {eng},
number = {1},
pages = {47-58, electronic only},
title = {Equivalent or absolutely continuous probability measures with given marginals},
url = {http://eudml.org/doc/270847},
volume = {3},
year = {2015},
}
TY - JOUR
AU - Patrizia Berti
AU - Luca Pratelli
AU - Pietro Rigo
AU - Fabio Spizzichino
TI - Equivalent or absolutely continuous probability measures with given marginals
JO - Dependence Modeling
PY - 2015
VL - 3
IS - 1
SP - 47
EP - 58, electronic only
AB - 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.
LA - eng
KW - Coupling; Domination on rectangles; Equivalent martingale measure; Finitely additive probability
measure; Mass transportat; coupling; domination on rectangles; equivalent martingale measure; finitely additive probability measure; mass transportat
UR - http://eudml.org/doc/270847
ER -
References
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- [2] Berti, P., L. Pratelli, and P. Rigo (2015). Two versions of the fundamental theorem of asset pricing. Electron. J. Probab. 20, 1–21. [WoS][Crossref] Zbl1326.60007
- [3] Bhaskara Rao, K. P. S. and M. Bhaskara Rao (1983). Theory of Charges. Academic Press, New York. Zbl0516.28001
- [4] Folland, G. B. (1984). Real Analysis: Modern Techniques and their Applications. Wiley, New York. Zbl0549.28001
- [5] Korman, J. and R. J. McCann (2015). Optimal transportation with capacity constraints. Trans. Amer. Math. Soc. 367(3), 1501– 1521. Zbl1305.90065
- [6] Ramachandran, D. (1979). Perfect Measures I and II. Macmillan, New Delhi. Zbl0523.60006
- [7] Ramachandran, D. (1996). Themarginal problem in arbitrary product spaces. In Distributions with fixed marginals and related topics, 260–272. Inst. Math. Statist., Hayward.
- [8] Strassen, V. (1965). The existence of probability measures with given marginals. Ann. Math. Statist 36, 423–439. [Crossref] Zbl0135.18701
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