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A note on comonotonic additivity

Published online by Cambridge University Press:  18 May 2009

June M. Parker
June M. Parker
Affiliation:
School of Mathematicsm University of Hull, Cottingham Road, Hull HU6 7Rx.
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Abstract

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The axiom of comonotonic independence for a preference ordering was introduced by Schmeidler [9]. It leads to the comonotonic additivity for the functional representing the preference ordering, which is necessarily a Choquet integral.

The aim of this paper is to illuminate the concepts of comonotonicity, comonotonic independence and comonotonic additivity. For example the seemingly weaker condition of weak comonotonic independence used by Chateauneuf in [2] is seen to be equivalent to comonotonic independence. Comonotonic additivity is characterized as additivity on chains of sets. From this the characterization of Choquet integrals in [4], [1], [8] follows easily.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 2 , May 1996 , pp. 199 - 205
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

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