 Stochastic comparison of random vectors with a common copulaMarco Scarsini and Alfred Müller Post-Print from HAL 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 invariant 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. Keywords: Directionally convex order; local mean preserving spread; copula; conditionally increasing random vectors; convex ordering; portfolio optimization (search for similar items in EconPapers) Published in Mathematics of Operations Research, 2001, Vol.26, N°4, pp. 723-740. ⟨10.1287/moor.26.4.723.10006⟩ There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00540198 DOI: 10.1287/moor.26.4.723.10006 Access Statistics for this paper More papers in Post-Print from HAL |
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