Dependence in a background risk model

Marie-Pier Côté and Christian Genest

Journal of Multivariate Analysis, 2019, vol. 172, issue C, 28-46

Abstract: Many copula families, including the classes of Archimedean, elliptical and Liouville copulas, may be written as the survival copula of a random vector R×(Y1,Y2), where R is a strictly positive random variable independent of the random vector (Y1,Y2) . A unified framework is presented for studying the dependence structure underlying this stochastic representation, which is called the background risk model. Formulas for the copula, Kendall’s tau and tail dependence coefficients are obtained and special cases are detailed. The usefulness of the construction for model building is illustrated with an extension of Archimedean copulas with completely monotone generators, based on the Farlie–Gumbel–Morgenstern copula. In particular, explicit expressions for the distribution and the Tail-Value-at-Risk of the aggregated risk RY1+RY2 are available in a generalization of the widely used multivariate Pareto-II model.

Keywords: Comonotonicity; Copula; Kendall’s tau; Laplace transform; Non-exchangeability; Radial symmetry; Random scaling; Risk aggregation; Tail dependence; Williamson transform (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (10)

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DOI: 10.1016/j.jmva.2018.11.012

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