Characterizations of Conditional Comonotonicity

Ka Chun Cheung
2007 Journal of Applied Probability  
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.
more » ... itioning σ-field. We also provide a new proof of a distributional representation and an almost sure representation of a conditionally comonotonic random vector.
doi:10.1017/s0021900200003302 fatcat:w3noahmcxzgkbhddo7haswswee