On the multidimensional extension of countermonotonicity and its applications

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<title>On the multidimensional extension of countermonotonicity and its applications</title>
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<namePart>Lee, Woojoo</namePart>
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<abstract displayLabel="Summary">In a 2-dimensional space, FréchetHoeffding upper and lower bounds define comonotonicity and countermonotonicity, respectively. Similarly, in the multidimensional case, comonotonicity can be defined using the FréchetHoeffding upper bound. However, since the multidimensional FréchetHoeffding lower bound is not a distribution function, there is no obvious extension of countermonotonicity in multidimensions. 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.

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<note type="statement of responsibility">Woojoo Lee, Jae Youn Ahn</note>
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<title>Insurance : mathematics and economics</title>
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<publisher>Oxford : Elsevier, 1990-</publisher>
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<identifier type="issn">0167-6687</identifier>
<identifier type="local">MAP20077100574</identifier>
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<text>05/05/2014 Volumen 56 Número 1 - mayo 2014 </text>
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