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Conglomerability and representations

Author

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  • Gianluca Cassese

Abstract

We prove results concerning the representation of a given distribution by means of a given random quantity. The existence of a solution to this problem is related to the notion of conglomerability, originally introduced by Dubins. We show that this property has many interesting applications in probability as well as in analysis. Based on it we prove versions of the extremal representation theorem of Choquet and of Skhorohod theorem.

Suggested Citation

  • Gianluca Cassese, 2015. "Conglomerability and representations," Working Papers 318, University of Milano-Bicocca, Department of Economics, revised 16 Dec 2015.
    • Handle: RePEc:mib:wpaper:318
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    File URL: http://repec.dems.unimib.it/repec/pdf/mibwpaper318.pdf
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    References listed on IDEAS

    as
    1. Karandikar, Rajeeva L., 1988. "A general principle for limit theorems in finitely additive probability: The dependent case," Journal of Multivariate Analysis, Elsevier, vol. 24(2), pages 189-206, February.
    2. Berti, Patrizia & Pratelli, Luca & Rigo, Pietro, 2006. "Asymptotic behaviour of the empirical process for exchangeable data," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 337-344, February.
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    Cited by:

    1. Michael Nielsen, 2019. "On linear aggregation of infinitely many finitely additive probability measures," Theory and Decision, Springer, vol. 86(3), pages 421-436, May.
    2. Gianluca Cassese, 2021. "Complete and competitive financial markets in a complex world," Finance and Stochastics, Springer, vol. 25(4), pages 659-688, October.
    3. Gianluca Cassese, 2019. "Nonparametric Estimates Of Option Prices And Related Quantities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(07), pages 1-29, November.

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    More about this item

    Keywords

    Choquet integral representation; Conglomerability; Distribution; Riesz representation; Skhorohod representation; Vector lattice;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

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