The Rearrangement Algorithm (RA) is an algorithm which has been introduced in [1] to compute numerically sharp lower and upper bounds on the distribution of a function of a number of dependent random variables having fixed marginal distributions. 

NEW: Python package by Karl Besser

The algorithm has been then developed further to:

 - compute sharp bounds for the VaR/ES of high-dimensional portfolios having fixed marginal distributions; see [2], [3].

 - compute sharp lower and upper bounds on the expected value of a supermodular function of d random variables having fixed marginal distributions; see [4].

NEW ARTICLE: Implementing the Rearrangement Algorithm: An Example from Computational Risk Management

SLIDES ILLUSTRATING THE ALGORITHM

Objectives:

This wepbage aims at becoming a forum of discussions on further developments and applications of the RA, and would like to offer sample codes, examples, assistance and troubleshooting for practitioners using the algorithm in quantitative risk management. 

In particular, we would like to have the following questions/open problems discussed/addressed:

• A proof of convergence of the RA remains an open problem.

• The RA might be a breaktrough for a particular type of bottleneck assignment problem; see the OR framework page.

References:

[1] Puccetti, G. andL. Rüschendorf (2012). Computation of sharp bounds on the distribution of a function of dependent risks. J. Comp. Appl. Math., 236 (7), 1833-1840. paper -preprint

[2] Embrechts, P., Puccetti, G. and L. Rüschendorf (2013). Model uncertainty and VaR aggregation. J. Bank. Financ., 37(8), 2750-2764. paper - post-print (updated) version

[3] Puccetti, G. (2013). Sharp bounds on the expected shortfall for a sum of dependent random variables. Stat. Probabil. Lett., 83(4), 1227-1232 paper - preprint

[4] Puccetti, G. and L. Rüschendorf (2015). Computation of sharp bounds on the expected value of a supermodular function of risks with given marginals. Commun. Stat. Simulat., 44 (3), 705-718. SSRN paper