n-Monotone exact functionals
Copyright policy )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 the notions of 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.
- Rey Juan Carlos University Spain
- King Juan Carlos University Spain
- Durham University United Kingdom
- Ghent University Belgium
Lower prevision, Risk measure, exact functional, Axioms; other general questions in probability, Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures, lower prevision, FOS: Mathematics, Comonotone additivity, Exact functional, set function, Applied Mathematics, Probability (math.PR), n-Monotonicity, Set functions and measures on spaces with additional structure, Functional Analysis (math.FA), Mathematics - Functional Analysis, Natural extension, monotone, Choquet integral, Coherence, coherent, Analysis, Mathematics - Probability
Lower prevision, Risk measure, exact functional, Axioms; other general questions in probability, Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures, lower prevision, FOS: Mathematics, Comonotone additivity, Exact functional, set function, Applied Mathematics, Probability (math.PR), n-Monotonicity, Set functions and measures on spaces with additional structure, Functional Analysis (math.FA), Mathematics - Functional Analysis, Natural extension, monotone, Choquet integral, Coherence, coherent, Analysis, Mathematics - Probability
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