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Choquet Integration on Riesz Spaces and Dual Comonotonicity

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Listed:
  • Simone Cerreia-Vioglio
  • Fabio Maccheroni
  • Massimo Marinacci
  • Luigi Montrucchio

Abstract

We give a general integral representation theorem (Theorem 6) for nonadditive functionals de?ned on an Archimedean Riesz space X with order unit. Additivity is replaced by a weak form of modularity, or equivalently dual comonotonic additivity, and integrals are Choquet integrals. Those integrals are de?ned through the Kakutani [8] isometric identi?cation of X with a C (K) space. We further show that our novel notion of dual comonotonicity naturally generalizes and characterizes the notions of comonotonicity found in the literature when X is assumed to be a space of functions.

Suggested Citation

  • Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2012. "Choquet Integration on Riesz Spaces and Dual Comonotonicity," Working Papers 433, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    • Handle: RePEc:igi:igierp:433
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    References listed on IDEAS

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    1. ZHOU, Lin, 1996. "Integral Representation of Continuous Comonotonically Additive Functionals," LIDAM Discussion Papers CORE 1996005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2010. "Singed Integral Representations of Comonotonic Additive Functionals," Working Papers 366, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    3. Itzhak Gilboa, 2004. "Uncertainty in Economic Theory," Post-Print hal-00756317, HAL.
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