n-Monotone exact functionals

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 n...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2008-11, Vol.347 (1), p.143-156
Main Authors: de Cooman, Gert, Troffaes, Matthias C.M., Miranda, Enrique
Format: Article
Language:English
Subjects:
Choquet integral
Coherence
Comonotone additivity
Exact functional
Exact sciences and technology
Lower prevision
Mathematical analysis
Mathematics
Measure and integration
n-Monotonicity
Natural extension
Risk measure
Sciences and techniques of general use
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2008.05.071