On the multidimensional extension of countermonotonicity and its applications
- 주제(키워드) Countermonotonicity , Comonotonicity , Minimal copula , Measures of concordance , Herd behavior index
- 등재 SCIE, SSCI, SCOPUS
- 발행기관 ELSEVIER SCIENCE BV
- 발행년도 2014
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000091696
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.insmatheco.2014.03.002
초록/요약
In a 2-dimensional space, Frechet-Hoeffding upper and lower bounds define comonotonicity and countermonotonicity, respectively. Similarly, in the multidimensional case, comonotonicity can be defined using the Frechet-Hoeffding upper bound. However, since the multidimensional Frechet-Hoeffding lower bound is not a distribution function, there is no obvious extension of countermonotonicity in multi-dimensions. This paper investigates in depth a new multidimensional extension of countermonotonicity. We first provide an equivalent condition for countermonotonicity in 2-dimension, and extend the definition of countermonotonicity into multidimensions. In order to justify such extensions, we show that newly defined countermonotonic copulas constitute a minimal class of copulas. Two applications will be provided. First, we will study the relationships between multidimensional countermonotonicity and such well-known multivariate concordance measures as Kendall's tau or Spearman's rho. Second, we will give a financial interpretation of multidimensional countermonotonicity via the existing herd behavior index. (C) 2014 Elsevier B.V. All rights reserved.
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