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1 results

  • Characterizations of Conditional Comonotonicity

  • Part of
  • Ka Chun Cheung
  • Journal:
    Journal of Applied Probability / Volume 44 / Issue 3 / September 2007
    Published online by Cambridge University Press:
    14 July 2016, pp. 607-617
    Print publication:
    September 2007
    • Article
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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.