Journal of Applied Probability

On the singular components of a copula

Fabrizio Durante, Juan Fernández-Sánchez, and Wolfgang Trutschnig

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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.

Article information

J. Appl. Probab. Volume 52, Number 4 (2015), 1175-1182.

First available in Project Euclid: 22 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E05: Distributions: general theory
Secondary: 28A50: Integration and disintegration of measures 91G70: Statistical methods, econometrics

Copula coupling disintegration theorem Markov kernel singular measure


Durante, Fabrizio; Fernández-Sánchez, Juan; Trutschnig, Wolfgang. On the singular components of a copula. J. Appl. Probab. 52 (2015), no. 4, 1175--1182. doi:10.1239/jap/1450802760.

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