n-Monotone exact functionals

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

Abstract

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.

Citation

de Cooman, G., Troffaes, M., & Miranda, E. (2008). n-Monotone exact functionals. Journal of Mathematical Analysis and Applications, 347(1), 143-156. https://doi.org/10.1016/j.jmaa.2008.05.071

• 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
• DOI: https://doi.org/10.1016/j.jmaa.2008.05.071
• Keywords: n-Monotonicity, Coherence, Natural extension, Choquet integral, Comonotone additivity, Exact functional, Lower prevision, Risk measure
• Public URL: https://durham-repository.worktribe.com/output/1548067