Rearrangement Algorithm

Python implementation of a rearrangement algorithm that can be used to calculate bounds on the value-at-risk (VaR) of dependent risks.

The current version includes the following calculations:

• Upper and lower bounds on the VaR of dependent risks¹
• Upper and lower bounds on the survival probability of functions of dependent risks²
• Upper and lower bounds on the expected value of supermodular functions of dependent risks³

Mathematical Background

Mathematical details and derivations can be found in the publications¹²³.

More information and an overview of extensions can be found on the website of the Rearrangement Algorithm project.

Implementation

Parts of this implementation are based on the qrmtools R package (version 0.0-13) by M. Hofert, K. Hornik, and A. J. McNeil. Details on the algorithm and the R implementation can be found in the paper "Implementing the Rearrangement Algorithm: An Example from Computational Risk Management", M. Hofert, In: Risks, vol. 8, no. 2, 2020⁴.

Installation

You can install the package via pip

pip install rearrangement-algorithm

If you want to install the latest (unstable) version, you can install the package from source

git clone https://gitlab.com/klb2/rearrangement-algorithm.git
cd rearrangement-algorithm
git checkout dev
pip install .

Documentation

You can find the documentation for this package on Read the Docs.
This also includes some usage examples.

License and Referencing

This program is licensed under the GPLv3 license. If you in any way use this code for research that results in publications, please cite this package.

Parts of this code are based on the qrmtools R package (version 0.0-13), which is also released under the GPLv3 license.

References

Footnotes

1. P. Embrechts, G. Puccetti, and L. Rüschendorf, "Model uncertainty and VaR aggregation," J. Bank. Financ., vol. 37, no. 8, pp. 2750-2764, Aug. 2013. doi:10.1016/j.jbankfin.2013.03.014 ↩ ↩²

2. G. Puccetti and L. Rüschendorf, "Computation of sharp bounds on the distribution of a function of dependent risks," J. Comput. Appl. Math., vol. 236, no. 7, pp. 1833-1840, Jan. 2012. doi:10.1016/j.cam.2011.10.015 ↩ ↩²

3. G. Puccetti and L. Rüschendorf, "Computation of Sharp Bounds on the Expected Value of a Supermodular Function of Risks with Given Marginals," Commun. Stat. - Simul. Comput., vol. 44, no. 3, pp. 705-718, Mar. 2015. doi:10.1080/03610918.2013.791368 ↩ ↩²

4. M. Hofert, "Implementing the Rearrangement Algorithm: An Example from Computational Risk Management," Risks, vol. 8, no. 2, May 2020. doi:10.3390/risks8020047 ↩