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Multivariate countermonotonicity and the minimal copulas

Title
Multivariate countermonotonicity and the minimal copulas
Authors
Lee W.Cheung K.C.Ahn J.Y.
Ewha Authors
안재윤
SCOPUS Author ID
안재윤scopus
Issue Date
2017
Journal Title
Journal of Computational and Applied Mathematics
ISSN
0377-0427JCR Link
Citation
vol. 317, pp. 589 - 602
Keywords
ComonotonicityCountermonotonicityMinimal copulaVariance minimization
Publisher
Elsevier B.V.
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
Fréchet–Hoeffding upper and lower bounds play an important role in various bivariate optimization problems because they are the maximum and minimum of bivariate copulas in concordance order, respectively. However, while the Fréchet–Hoeffding upper bound is the maximum of any multivariate copulas, there is no minimum copula available for dimensions d≥3. Therefore, multivariate minimization problems with respect to a copula are not straightforward as the corresponding maximization problems. When the minimum copula is absent, minimal copulas are useful for multivariate minimization problems. We illustrate the motivation of generalizing the joint mixability to d-countermonotonicity defined in Lee and Ahn (2014) through variance minimization problems and show that d-countermonotonic copulas are minimal copulas. © 2017 Elsevier B.V.
DOI
10.1016/j.cam.2016.12.032
Appears in Collections:
자연과학대학 > 통계학전공 > Journal papers
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