hal-00540198
https://hec.hal.science/hal-00540198
doi:10.1287/moor.26.4.723.10006
[SHS] Sciences de l'Homme et de la Société
[HEC] HEC Paris
[CNRS] CNRS - Centre national de la recherche scientifique
[AO-ECONOMIE] Archives ouvertes de l'Economie
Stochastic comparison of random vectors with a common copula
Scarsini, Marco
Muller, Alfred
[SHS.ECO.ECO] Humanities and Social Sciences/Economics and Finance/domain_shs.eco.eco
ART
Directionally convex order
local mean preserving spread
copula
conditionally increasing random vectors
convex ordering
portfolio optimization
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.
2001
en
Mathematics of Operations Research
INFORMS