Grouped normal variance mixtures are a class of multivariate distributions that generalize classical normal variance mixtures such as the multivariate t distribution, by allowing different groups to have different (comonotone) mixing distributions. This allows one to better model risk factors...

The new class of matrix-tilted Archimedean copulas is introduced. It combines properties of Archimedean and elliptical copulas by introducing a tilting matrix in the stochastic representation of Archimedean copulas, similar to the Cholesky factor for elliptical copulas. Basic properties of this...

In this paper, we propose a novel framework for estimating systemic risk measures and risk allocations based on Markov Chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution...

This article considers risk measures constructed under a discrete mixture-of-normal distribution on the innovations of a GARCH model with time-varying volatility. The authors use an approach based on a continuous empirical characteristic function to estimate the parameters of the model using...