Multivariate countermonotonicity and the minimal copulas
- 주제(키워드) Comonotonicity , Countermonotonicity , Minimal copula , Variance minimization
- 등재 SCIE, SCOPUS
- 발행기관 Elsevier B.V.
- 발행년도 2017
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000141812
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.cam.2016.12.032
- 저작권 이화여자대학교 논문은 저작권에 의해 보호받습니다.
초록/요약
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.
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