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n-Monotone exact functionals

de Cooman, Gert; Troffaes, Matthias; Miranda, Enrique

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Gert de Cooman

Enrique Miranda


We study n-monotone functionals, which constitute a generalisation of n-monotone set functions. We investigate their relation to the concepts of exactness and natural extension, which generalise coherence and natural extension in the behavioural theory of imprecise probabilities. We improve upon a number of results in the literature, and prove among other things a representation result for exact n-monotone functionals in terms of Choquet integrals.


de Cooman, G., Troffaes, M., & Miranda, E. (2008). n-Monotone exact functionals. Journal of Mathematical Analysis and Applications, 347(1), 143-156.

Journal Article Type Article
Publication Date Nov 1, 2008
Deposit Date Jan 16, 2015
Publicly Available Date Jan 16, 2015
Journal Journal of Mathematical Analysis and Applications
Print ISSN 0022-247X
Electronic ISSN 1096-0813
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 347
Issue 1
Pages 143-156
Keywords n-Monotonicity, Coherence, Natural extension, Choquet integral, Comonotone additivity, Exact functional, Lower prevision, Risk measure


Accepted Journal Article (231 Kb)

Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of mathematical analysis and applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of mathematical analysis and applications, 347/1, 2008, 10.1016/j.jmaa.2008.05.071

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