IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v23y2014i4p501-518.html
   My bibliography  Save this article

On the equivalence of conglomerability and disintegrability for unbounded random variables

Author

Listed:
  • Mark Schervish
  • Teddy Seidenfeld
  • Joseph Kadane

Abstract

We extend a result of Dubins (Ann Probab 3:89–99, 1975 ) from bounded to unbounded random variables. Dubins showed that a finitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the marginal expectation is always within the smallest closed interval containing the conditional expectations (conglomerability). We give a sufficient condition to extend this result to collections of random variables that have finite expected value and whose conditional expectations are finite and have finite expected value. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stmapp:v:23:y:2014:i:4:p:501-518
    DOI: 10.1007/s10260-014-0282-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10260-014-0282-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10260-014-0282-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Seidenfeld, Teddy & Schervish, Mark J. & Kadane, Joseph B., 2009. "Preference for equivalent random variables: A price for unbounded utilities," Journal of Mathematical Economics, Elsevier, vol. 45(5-6), pages 329-340, May.
    3. L. Crisma & P. Gigante, 2001. "A notion of coherent conditional prevision for arbitrary random quantities," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 29-40, January.
    4. L. Crisma & P. Gigante & P. Millossovich, 1997. "A notion of coherent revision for arbitrary random quantities," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(3), pages 233-243, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Vantaggi, Barbara, 2010. "Incomplete preferences on conditional random quantities: Representability by conditional previsions," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 104-112, September.
    3. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2013. "Finitely Additive Equivalent Martingale Measures," Journal of Theoretical Probability, Springer, vol. 26(1), pages 46-57, March.
    4. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, vol. 77(1), pages 31-83, June.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Pierpaolo Angelini, 2024. "Extended Least Squares Making Evident Nonlinear Relationships between Variables: Portfolios of Financial Assets," JRFM, MDPI, vol. 17(8), pages 1-24, August.
    10. Pierpaolo Angelini, 2024. "Invariance of the Mathematical Expectation of a Random Quantity and Its Consequences," Risks, MDPI, vol. 12(1), pages 1-17, January.
    11. Russell, Jeffrey Sanford, 2020. "Non-Archimedean preferences over countable lotteries," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 180-186.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stmapp:v:23:y:2014:i:4:p:501-518. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.