Choquet Integration on Riesz Spaces and Dual Comonotonicity

Simone Cerreia-Vioglio, Fabio Maccheroni, Massimo Marinacci and Luigi Montrucchio

No 433, Working Papers from IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University

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.

Date: 2012
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