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Strong previsions of random elements

Author

Listed:
  • Patrizia Berti

    (Università di Modena)

  • Eugenio Regazzini

    (Università di Pavia)

  • Pietro Rigo

    (Università di Pavia)

Abstract

LetC be a class of arbitrary real random elements andP an extended real valued function onC. Two definitions of coherence forP are compared. Both definitions reduce to the classical de Finetti's one whenC includes bounded random elements only. One of the two definitions (called strong coherence) is investigated, and some criteria for checking it are provided. Moreover, conditions are given for the integral representation of a coherentP, possibly with respect to a δ-additive probability. Finally, the two definitions and the integral representation theorems are extended to the case whereC is a class of random elements taking values in a given Banach space.

Suggested Citation

  • Patrizia Berti & Eugenio Regazzini & Pietro Rigo, 2001. "Strong previsions of random elements," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 11-28, January.
    • Handle: RePEc:spr:stmapp:v:10:y:2001:i:1:d:10.1007_bf02511636
    DOI: 10.1007/BF02511636
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    References listed on IDEAS

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    1. Clark, Stephen A., 1993. "The valuation problem in arbitrage price theory," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 463-478.
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    Cited by:

    1. Mark J. Schervish & Teddy Seidenfeld & Joseph B. Kadane, 2014. "On the equivalence of conglomerability and disintegrability for unbounded random variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(4), pages 501-518, November.
    2. Mark Schervish & Teddy Seidenfeld & Joseph Kadane, 2014. "On the equivalence of conglomerability and disintegrability for unbounded random variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(4), pages 501-518, November.
    3. Pierpaolo Angelini, 2024. "Invariance of the Mathematical Expectation of a Random Quantity and Its Consequences," Risks, MDPI, vol. 12(1), pages 1-17, January.
    4. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2010. "Finitely Additive Equivalent Martingale Measures," Quaderni di Dipartimento 123, University of Pavia, Department of Economics and Quantitative Methods.
    5. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2013. "Finitely Additive Equivalent Martingale Measures," Journal of Theoretical Probability, Springer, vol. 26(1), pages 46-57, March.
    6. Pierpaolo Angelini, 2020. "A Portfolio of Risky Assets and Its Intrinsic Properties," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(3), pages 1-61, June.
    7. Vantaggi, Barbara, 2010. "Incomplete preferences on conditional random quantities: Representability by conditional previsions," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 104-112, September.
    8. Pierpaolo Angelini & Fabrizio Maturo, 2020. "Non-Parametric Probability Distributions Embedded Inside of a Linear Space Provided with a Quadratic Metric," Mathematics, MDPI, vol. 8(11), pages 1-17, October.
    9. Pierpaolo Angelini & Fabrizio Maturo, 2022. "The consumer’s demand functions defined to study contingent consumption plans," Quality & Quantity: International Journal of Methodology, Springer, vol. 56(3), pages 1159-1175, June.

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