Invariant dependence structure under univariate truncation

Fabrizio Durante · Piotr Jaworski

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Financial Risk and Volatility Modeling Statistical Distribution Estimation and Applications Probability and Risk Models

Abstract

The class of all bivariate copulas that are invariant under univariate truncation is characterized. To this end, a family of bivariate copulas generated by a real-valued function is introduced. The obtained results are also used in order to show that the Clayton family of copulas (including its limiting elements) coincides with the class of copulas that are invariant under bivariate truncation and contains all exchangeable copulas which are invariant under univariate truncation.

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References

1999An Introduction to Copulas 2005Quantitative Risk Management: Concepts, Techniques, and Tools 2007The t Copula and Related Copulas 2006An Introduction to Copulas (Springer Series in Statistics)2010Copula Theory and Its Applications 2014Extremes in Nature: An Approach Using Copulas 1986Copules archimédiennes et families de lois bidimensionnelles dont les marges sont données 2010Copula Theory: An Introduction

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2013Multivariate patchwork copulas: A unified approach with applications to partial comonotonicity

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