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...

After a brief overview of aspects of computational risk management, the implementation of the rearrangement algorithm in R is considered as an example from computational risk management practice. This algorithm is used to compute the largest quantile (worst value-at-risk) of the sum of the...

This paper presents an intellectual exchange with ChatGPT, an artificial intelligence chatbot, about correlation pitfalls in risk management. The exchange takes place in the form of a conversation that provides ChatGPT with context. The purpose of this conversation is to evaluate ChatGPT's...

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...