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Characterizations of Conditional Comonotonicity

Part of: Multivariate analysis Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Ka Chun Cheung
Ka Chun Cheung*
Affiliation:
University of Calgary
*
∗Postal address: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T3A 2E2, Canada. Email address: [email protected]
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Abstract

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The notion of conditional comonotonicity was first used implicitly by Kaas, Dhaene, and Goovaerts (2000) and was formally introduced by Jouini and Napp (2004) as a generalization of the classical concept of comonotonicity. The objective of the present paper is to further investigate this relatively new concept. The main result is that a random vector is comonotonic conditional to a certain σ-field if and only if it is almost surely comonotonic locally on each atom of the conditioning σ-field. We also provide a new proof of a distributional representation and an almost sure representation of a conditionally comonotonic random vector.

Keywords

Comonotonicityconditional comonotonicitylocal comonotonicityregular conditional distributionprojection theoremmeasurable graph theorem

MSC classification

Secondary: 60E99: None of the above, but in this section 62H20: Measures of association (correlation, canonical correlation, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 3 , September 2007 , pp. 607 - 617
Copyright
Copyright © Applied Probability Trust 2007 

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