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On the singular components of a copula

  • Fabrizio Durante (a1), Juan Fernández-Sánchez (a2) and Wolfgang Trutschnig (a3)
Abstract

We analyze copulas with a nontrivial singular component by using their Markov kernel representation. In particular, we provide existence results for copulas with a prescribed singular component. The constructions not only help to deal with problems related to multivariate stochastic systems of lifetimes when joint defaults can occur with a nonzero probability, but even provide a copula maximizing the probability of joint default.

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Corresponding author
Postal address: Faculty of Economics and Management, Free University of Bozen-Bolzano, Bolzano, Italy. Email address: fabrizio.durante@unibz.it
∗∗ Postal address: Grupo de Investigación de Análisis Matemático, Universidad de Almería, La Cañada de San Urbano, Almería, Spain. Email address: juan.fernandez@ual.es
∗∗∗ Postal address: Department for Mathematics, University of Salzburg, Salzburg, Austria. Email address: wolfgang@trutschnig.net
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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