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n-Monotone exact functionals.

de Cooman, Gert and Troffaes, Matthias and Miranda, Enrique (2008) 'n-Monotone exact functionals.', Journal of mathematical analysis and applications., 347 (1). pp. 143-156.


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.

Item Type:Article
Keywords:n-Monotonicity, Coherence, Natural extension, Choquet integral, Comonotone additivity, Exact functional, Lower prevision, Risk measure
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Publisher 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
Date accepted:No date available
Date deposited:16 January 2015
Date of first online publication:November 2008
Date first made open access:No date available

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