Paper Info
Title
Stochastic Comparison of Random Vectors with a Common Copula
Abstract
We consider two random vectorsX andY, such that the components of脗 脗 X are dominated in the convex order by the corresponding components of脗 脗 Y. We want to find conditions under which this implies that any positive linear combination of the components of脗 脗 X is dominated in the convex order by the same positive linear combination of the components of脗 脗 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 vectorsX andY, 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 byY 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.
Year
DOI
Venue
2001
10.1287/moor.26.4.723.10006
Math. Oper. Res.
Keywords
DocType
Volume
Common Copula,Stochastic Comparison,common copula,copula,convex ordering,directionally convex order,new concept,conditionally increasing random vectors,local mean preserving spread,convex order,random vectorsX andY,portfolio optimization. 723,positive linear combination,dependence structure,portfolio optimization problem,corresponding component,random vector,Random Vectors
Journal
26
Issue
ISSN
Citations 
4
0364-765X
17
PageRank 
References 
Authors
2.46
3
2
Name
Order
Citations
PageRank
Alfred Müller18717.12
Marco Scarsini216433.96