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Bivariate copula decomposition in terms of comonotonicity, countermonotonicity and independence. (English) Zbl 1098.62070
Summary: Copulas are statistical tools for modelling the multivariate dependence structure among variables in a distribution free way. This paper investigates bivariate copula structure; the existence and uniqueness of a bivariate copula decomposition into a comonotonic, an independent, a countermonotonic, and an indecomposable part are proved, while the coefficients are determined from partial derivatives of the corresponding copula. Moreover, for the indecomposable part, an optimal convex approximation is provided and analyzed on the basis of the usual criterion. Some applications of the decomposition in finance and insurance are mentioned.

##### MSC:
 62H05 Characterization and structure theory for multivariate probability distributions; copulas 62G99 Nonparametric inference 62P05 Applications of statistics to actuarial sciences and financial mathematics 62H20 Measures of association (correlation, canonical correlation, etc.)
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