Equivalent or absolutely continuous probability measures with given marginals

• Autorzy: Patrizia Berti , Luca Pratelli , Pietro Rigo , Fabio Spizzichino
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Coupling; Domination on rectangles; Equivalent martingale measure; Finitely additive probabilitymeasure; Mass transportat

Kategorie tematyczne

• 60A05: Axioms; other general questions
• 60A10: Probabilistic measure theory
• 28A35: Measures and integrals in product spaces

• Wydawca: De Gruyter Open
• Czasopismo: Dependence Modeling
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-02-21

zaakceptowano

2015-05-07

online

2015-05-25

Twórcy

autor

Patrizia Berti

• Dipartimento di Matematica Pura ed Applicata ”G. Vitali”, Universita’ di Modena e Reggio-Emilia, via Campi
  213/B, 41100 Modena, Italy,

autor

Luca Pratelli

• Accademia Navale, viale Italia 72, 57100 Livorno, Italy

autor

Pietro Rigo

• Dipartimento di Matematica ”F. Casorati”, Universita’
  di Pavia, via Ferrata 1, 27100 Pavia, Italy

autor

Fabio Spizzichino

• Dipartimento di Matematica ”G. Castelnuovo”, Universita’ di Roma ”La Sapienza”, piazzale
  A. Moro 5, 00185 Roma, Italy

Bibliografia

• [1] Berti, P., L. Pratelli, and P. Rigo (2014). A unifying view on some problems in probability and statistics. Stat. Methods Appl. 23(4), 483–500. [Crossref][WoS]
• [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]
• [3] Bhaskara Rao, K. P. S. and M. Bhaskara Rao (1983). Theory of Charges. Academic Press, New York.
• [4] Folland, G. B. (1984). Real Analysis: Modern Techniques and their Applications. Wiley, New York.
• [5] Korman, J. and R. J. McCann (2015). Optimal transportation with capacity constraints. Trans. Amer. Math. Soc. 367(3), 1501– 1521.
• [6] Ramachandran, D. (1979). Perfect Measures I and II. Macmillan, New Delhi.
• [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]

Identyfikatory

DOI

10.1515/demo-2015-0004