Stochastic comparison of random vectors with a common copula

Stochastic comparison of random vectors with a common copula

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Article ID: iaor20041359
Country: United States
Volume: 26
Issue: 4
Start Page Number: 723
End Page Number: 740
Publication Date: Nov 2001
Journal: Mathematics of Operations Research
Authors: ,
Abstract:

We consider two random vectors X and Y, such that the components of X are dominated in the convex order by the corresponding components of Y. We want to find conditions under which this implies that any positive linear combination of the components of X is dominated in the convex order by the same positive linear combination of the components of Y. This problem has a motivation in the comparison of portfolios in terms of risk. The conditions for the above dominance will concern the dependence structure of the two random vectors X and Y, namely, the two random vectors will have a common copula and will be conditionally increasing. This new concept of dependence is strictly related to the idea of conditionally increasing in sequence, but, in addition, it is invariannt under permutation. We will actually prove that, under the above conditions, X will be dominated by Y in the directionally convex order, which yields as a corollary the dominance for positive linear combinations. This result will be applied to a portfolio optimization problem.

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