Bounds for Distorted Risk Measures

Gonçalves, Marcelo Neves; Kolev, Nikolai; Fabris, Antonio Elias

doi:10.1515/eqc.2008.243

Cited by 2 publications

(1 citation statement)

References 11 publications

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“…Other areas related to (quasi-)copulas are generalized integration theory [37,41,42], The support by the "Technologie-Transfer-Förderung" of the Upper Austrian Government (Wi-2014-200710/13-Kx/Kai) is gratefully acknowledged, as well as the support by the Slovak Grants APVV-14-0013, VEGA 1/0614/18 and VEGA 1/0891/17. B Erich Peter Klement ep.klement@jku.at Extended author information available on the last page of the article decision theory [77], finance [7,27], preference modeling [9,13], but also fuzzy logics and the theory of fuzzy sets [10,30,63].…”

Section: Introductionmentioning

confidence: 99%

The key role of convexity in some copula constructions

Saminger‐Platz

Kolesárová

Mesiar

et al. 2019

European Journal of Mathematics

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We start with some binary ("outer") copula, apply it to an arbitrary binary ("inner") copula and its dual (the latter being transformed by some real function) and ask under which conditions the result is again a binary copula. Sufficient convexity conditions for the transformation function and for the "outer" copula (ultramodularity and Schur concavity) are given, thus generalizing the scenarios considered in Klement et al.

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Section: Introductionmentioning

confidence: 99%

The key role of convexity in some copula constructions

Saminger‐Platz

Kolesárová

Mesiar

et al. 2019

European Journal of Mathematics

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On the role of ultramodularity and Schur concavity in the construction of binary copulas

Klement¹,

Kolesárová²,

Mesiar³

et al. 2017

Journal of Mathematical Inequalities

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Abstract. We discuss and stress the role of ultramodularity and Schur concavity in special types of constructions of copulas. After recalling some known ultamodularity-based results, we focus on the so-called D -product of a copula and its dual. We show that for each copula D which is ultramodular and Schur concave on the left upper triangle of the unit square, this D -product of an arbitrary copula and its dual is again a copula. Several examples and counterexamples are given. Finally, some of our results are generalized to the case of semicopulas and quasi-copulas. Mathematics subject classification (2010): 26B25, 26D20, 62H05.

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Bounds for Distorted Risk Measures

Cited by 2 publications

References 11 publications

The key role of convexity in some copula constructions

The key role of convexity in some copula constructions

On the role of ultramodularity and Schur concavity in the construction of binary copulas

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