We study the problem of finding the worst-case joint distribution of a set of risk factors given prescribed multivariate marginals with nonlinear loss function. The method has applications to any situation where marginals are provided, and bounds need to be determined on total portfolio risk....

The goal of this dissertation is to explore nested Archimedean copulas. In particular, efficient sampling algorithms, especially suited for large dimensions, are presented. As an application, a pricing model for collateralized debt obligations (CDOsʺ) is developed. Copulas are distribution...

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...

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...