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On the equivalence of conglomerability and disintegrability for unbounded random variables

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
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