Improved algorithms for computing worst Value-at-Risk

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 and may be of interest in any context in which it is required to find columnwise permutations of a matrix such that the minimal (maximal) row sum is maximized (minimized).

On some synchronization problems with multiple instances

“…The RA turns out to be very useful in operations research(Boudt, Jakobsons, and Vanduffel (2018)) and in insurance where it appears as a reference tool for assessing the uncertainty with respect to risk estimates of portfolios(Bernard, Rüschendorf, Vanduffel, and Wang (2017), Hofert, Memartoluie, Saunders, andWirjanto (2017)). …”