On heavy-tailed risks under Gaussian copula: the effects of marginal transformation

DOI10.1016/J.JMVA.2024.105310arXiv2304.05004MaRDI QIDQ6432708

Publication date: 11 April 2023

Abstract: In this paper, we compute multivariate tail risk probabilities where the marginal risks are heavy-tailed and the dependence structure is a Gaussian copula. The marginal heavy-tailed risks are modeled using regular variation which leads to a few interesting consequences. First, as the threshold increases, we note that the rate of decay of probabilities of tail sets vary depending on the type of tail sets considered and the Gaussian correlation matrix. Second, we discover that although any multivariate model with a Gaussian copula admits the so called asymptotic tail independence property, the joint tail behavior under heavier tailed marginal variables is structurally distinct from that under Gaussian marginal variables. The results obtained are illustrated using examples and simulations.

Mathematics Subject Classification ID

Statistical methods; risk measures (91G70) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Extreme value theory; extremal stochastic processes (60G70) Statistics of extreme values; tail inference (62G32) Multivariate analysis (62Hxx)