Diversity of Bivariate Concordance Measures

Martynas Manstavičius
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Martynas Manstavičius: Faculty of Mathematics and Informatics, Institute of Mathematics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, Lithuania

Mathematics, 2022, vol. 10, issue 7, 1-18

Abstract: We revisit the axioms of Scarsini, defining bivariate concordance measures for a pair of continuous random variables ( X , Y ) ; such measures can be understood as functions of the bivariate copula C associated with ( X , Y ) . Two constructions, investigated in the works of Edwards, Mikusiński, Taylor, and Fuchs, are generalized, yielding, in particular, examples of higher than degree-two polynomial-type concordance measures, along with examples of non-polynomial-type concordance measures, and providing an incentive to investigate possible further characterizations of such concordance measures, as was achieved by Edwards and Taylor for the degree-one case.

Keywords: scarsini axioms; bivariate copula; transformation; polynomial-type concordance measure; multiplicative function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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