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n-Monotone exact functionals |
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| Authors: | Gert de Cooman Enrique Miranda |
| Institution: | a Ghent University, SYSTeMS Research Group, Technologiepark - Zwijnaarde 914, 9052 Zwijnaarde, Belgium b Durham University, Department of Mathematical Sciences, Science Laboratories, South Road, Durham, DH1 3LE, UK c Rey Juan Carlos University, Department of Statistics and Operations Research, C-Tulipán s/n, 28933 Móstoles, Spain |
| 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. |
| Keywords: | n-Monotonicity Coherence Natural extension Choquet integral Comonotone additivity Exact functional Lower prevision Risk measure |
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