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On the singular components of a copula

Part of:Distribution theory - ProbabilityClassical measure theoryMathematical finance

Published online by Cambridge University Press:  30 March 2016

Fabrizio Durante,
Juan Fernández-Sánchez and
Wolfgang Trutschnig
Fabrizio Durante*
Affiliation:
Free University of Bozen-Bolzano
Juan Fernández-Sánchez*
Affiliation:
Universidad de Almería
Wolfgang Trutschnig*
Affiliation:
University of Salzburg
*
∗ 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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Abstract

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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.

Keywords

Copulacouplingdisintegration theoremMarkov kernelsingular measure

MSC classification

Primary:60E05: Distributions
Secondary:28A50: Integration and disintegration of measures91G70: Statistical methods, econometrics

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 52 , Issue 4 , December 2015, pp. 1175 - 1182
Copyright
Copyright © Applied Probability Trust 2015 

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