**The Rearrangement Algorithm project**

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.

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].

**Objectives:**

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. and

L. Rüschendorf (2012). Computation of sharp bounds on the distribution of a function of dependent risks. *J. Comp. Appl. Math., *236 (7), 1833-1840.* *

[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