Metadata-Version: 2.1
Name: rearrangement-algorithm
Version: 0.1.0
Summary: Implementation of the rearrangement algorithm
Home-page: https://gitlab.com/klb2/rearrangement-algorithm
Author: Karl Besser
Author-email: k.besser@tu-bs.de
License: GPLv3
Project-URL: Documentation, https://rearrangement-algorithm.readthedocs.io
Project-URL: Source Code, https://gitlab.com/klb2/rearrangement-algorithm
Keywords: rearrangement algorith,quantitative risk management
Platform: UNKNOWN
Description-Content-Type: text/markdown
License-File: LICENSE

# 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 risks[^embrechts2013]
- Upper and lower bounds on the survival probability of functions of dependent
  risks[^puccetti2012]
- Upper and lower bounds on the expected value of supermodular functions of
  dependent risks[^puccetti2015]


## Mathematical Background
Mathematical details and derivations can be found in the
publications[^embrechts2013][^puccetti2012][^puccetti2015].

More information and an overview of extension can be found on the website of
the [Rearrangement Algorithm
project](https://sites.google.com/site/rearrangementalgorithm/).



## Implementation
Parts of this implementation are based on the
[qrmtools](https://cran.r-project.org/package=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,
2020](https://doi.org/10.3390/risks8020047)[^hofert2020].



## 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](https://cran.r-project.org/package=qrmtools) R package (version
0.0-13), which is also released under the GPLv3 license.


## References
[^embrechts2013]: 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](https://doi.org/10.1016/j.jbankfin.2013.03.014)
[^puccetti2015]: 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](https://doi.org/10.1080/03610918.2013.791368)
[^puccetti2012]: 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](https://doi.org/10.1016/j.cam.2011.10.015)
[^hofert2020]: M. Hofert, "Implementing the Rearrangement Algorithm: An Example from Computational Risk Management," Risks, vol. 8, no. 2, May 2020. [doi:10.3390/risks8020047](https://doi.org/10.3390/risks8020047)


