n-Monotone exact functionals
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.
- Publication:
-
Journal of Mathematical Analysis and Applications
- Pub Date:
- November 2008
- DOI:
- 10.1016/j.jmaa.2008.05.071
- arXiv:
- arXiv:0801.1962
- Bibcode:
- 2008JMAA..347..143D
- Keywords:
-
- n-Monotonicity;
- Coherence;
- Natural extension;
- Choquet integral;
- Comonotone additivity;
- Exact functional;
- Lower prevision;
- Risk measure;
- Mathematics - Functional Analysis;
- Mathematics - Probability
- E-Print:
- Journal of Mathematical Analysis and Applications 347 (2008) 143-156