Improved Algorithms for Computing Worst Value-at-Risk: Numerical Challenges and the Adaptive Rearrangement Algorithm

Dr. Marius Hofert

University of Waterloo

About the Speaker

Marius Hofert obtained his PhD in Mathematics from University of Ulm in 2010 after completing a diploma in Mathematics and Management at University of Ulm and a master's degree in Mathematics at Syracuse University. He then held a postdoctoral research position (Willis Research Fellow) at RiskLab, ETH Zurich, under the supervision of Professor Paul Embrechts. After a guest professorship (W2) in the Department of Mathematics at Technische Universität München and a visiting assistant professorship in the Department of Applied Mathematics at University of Washington, he joined the Department of Statistics and Actuarial Science at University of Waterloo in July 2014.

Abstract

Numerical challenges inherent in algorithms for computing worst Value-at-Risk in homogeneous portfolios are identified and solutions as well as words of warning concerning their implementation are provided. Furthermore, both conceptual and computational improvements to the Rearrangement Algorithm for approximating worst Value-at-Risk for portfolios with arbitrary marginal loss distributions are given. In particular, a novel Adaptive Rearrangement Algorithm is introduced and investigated. These algorithms are implemented using the R package qrmtools.