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Choquet integration on Riesz spaces and dual comonotonicity

Authors: Simone Cerreia-Vioglio, Fabio Maccheroni, Massimo Marinacci and Luigi Montrucchio
Journal: Trans. Amer. Math. Soc. 367 (2015), 8521-8542
MSC (2010): Primary 28A12, 28A25, 28C05, 46B40, 46B42, 46G12
Published electronically: May 13, 2015
MathSciNet review: 3403064
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Abstract: We give a general integral representation theorem for nonadditive functionals defined on an Archimedean Riesz space $ X$ with unit. Additivity is replaced by a weak form of modularity, or, equivalently, dual comonotonic additivity, and integrals are Choquet integrals. Those integrals are defined through the Kakutani isometric identification of $ X$ with a $ C\left (K\right ) $ space. We further show that our 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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Additional Information

Simone Cerreia-Vioglio
Affiliation: Dipartimento di Scienze delle Decisioni and IGIER, Università Bocconi, via Sarfatti, 25 Milan, Italy

Fabio Maccheroni
Affiliation: Dipartimento di Scienze delle Decisioni and IGIER, Università Bocconi, via Sarfatti, 25 Milan, Italy

Massimo Marinacci
Affiliation: Dipartimento di Scienze delle Decisioni and IGIER, Università Bocconi, via Sarfatti, 25 Milan, Italy

Luigi Montrucchio
Affiliation: Collegio Carlo Alberto, Università di Torino, via Real Collegio 30, 10024 Moncalieri Torino, Italy

Received by editor(s): April 27, 2012
Received by editor(s) in revised form: September 29, 2013
Published electronically: May 13, 2015
Additional Notes: The financial support of ERC (Advanced Grant BRSCDP-TEA), AXA Research Fund, and MIUR (Grant PRIN 20103S5RN3_005) is gratefully acknowledged
Article copyright: © Copyright 2015 American Mathematical Society

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