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Choquet Integration on Riesz Spaces and Dual Comonotonicity

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  • 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.

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Bibliographic Info

Paper provided by IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University in its series Working Papers with number 433.

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Date of creation: 2012
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Handle: RePEc:igi:igierp:433

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