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Some Extensions of Singular Mixture Copulas

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Abstract

In Lauterbach (ZVersWiss, 101(5), 605–619, 2012) and Lauterbach and Pfeifer (Copulae in mathematical and quantitative finance, Springer, Dordrecht, 2013) the family of Singular Mixture Copulas was introduced. We present and discuss two extensions of these copulas. Both extensions are based on an approach introduced by Khoudraji (Contributions à l’étude des copules et à la modélisation des valeurs extrêmes bivariées. Ph.D. thesis, 1995). We study the dependence properties of the constructed copulas and show that the resulting copulas possess differing upper and lower tail dependence coefficients.

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Notes

  1. 1.

    See Nelsen (2006), Sect. 3.2.

  2. 2.

    See Dovgoshey et al. (2006) for more information about the Cantor function.

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Acknowledgments

The authors would like to sincerely thank the reviewers for their detailed comments, which led to an improvement of the presentation of this paper.

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Authors and Affiliations

  1. Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany

    Dominic Lauterbach & Dietmar Pfeifer

Authors
  1. Dominic Lauterbach
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  2. Dietmar Pfeifer
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Corresponding author

Correspondence to Dietmar Pfeifer .

Editor information

Editors and Affiliations

  1. European Centre for Advanced Research in Economics and Statistics, Université Libre de Bruxelles, Bruxelles, Belgium

    Marc Hallin

  2. Department of Applied Economics and Statistics, University of Delaware, Newark, Delaware, USA

    David M. Mason

  3. School of Mathematics and Science, Carl von Ossietzky University, Oldenburg, Germany

    Dietmar Pfeifer

  4. Mathematical Institute, University of Cologne, Köln, Germany

    Josef G. Steinebach

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Lauterbach, D., Pfeifer, D. (2015). Some Extensions of Singular Mixture Copulas. In: Hallin, M., Mason, D., Pfeifer, D., Steinebach, J. (eds) Mathematical Statistics and Limit Theorems. Springer, Cham. https://doi.org/10.1007/978-3-319-12442-1_15

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