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A strong law of large numbers for capacities

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Author Info

  • Fabio Maccheroni

    ()

  • Massimo Marinacci

    ()

Abstract

We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the lower and the upper Choquet integrals of the random variables, provided either the random variables or the capacity are continuous.

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File URL: http://www.icer.it/docs/wp2004/Maccheroni-Marinacci28-04.pdf
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Bibliographic Info

Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 28-2004.

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Length: 14 pages
Date of creation: Jun 2004
Date of revision:
Handle: RePEc:icr:wpmath:28-2004

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Related research

Keywords: Capacities; Choquet integral; Strong law of large numbers;

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Cited by:
  1. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini & Marco Taboga, 2009. "Portfolio Selection With Monotone Mean-Variance Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 487-521.
  2. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2006. "Recursive Smooth Ambiguity Preferences," Carlo Alberto Notebooks 17, Collegio Carlo Alberto, revised 2008.
  3. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.

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