Comonotonic Modification of Random Vector in Its Own Probability Space
7 Pages Posted: 31 Jan 2011
Date Written: January 9, 2011
For any random vector X = (X1; ...;Xn) on a given probability space (Ω;F;Pr), one can always instruct comonotonic modi cations of X, which are de ned as random vectors with the same marginals as X but with the comonotonic copula describing their dependency structure. In this short note, we investigate whether it is always possible or not to de necomonotonic modi cations of X on its own probability space (Ω;F; Pr).
Keywords: Comonotonic random vector, comonotonic modi cation, non-atomic probability space
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