The Rearrangement Algorithm of Puccetti and Rüschendorf: Proving the Convergence

Marcello Galeotti (), Giovanni Rabitti () and Emanuele Vannucci ()
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Marcello Galeotti: University of Florence, Department of Statistics, Informatics, Applications
Giovanni Rabitti: Bocconi University, Department of Decision Sciences
Emanuele Vannucci: University of Pisa, Department of Economics and Management

A chapter in Mathematical and Statistical Methods for Actuarial Sciences and Finance, 2018, pp 363-367 from Springer

Abstract: Abstract In 2012 Puccetti and Rüschendorf [J. Comp. Appl. Math., 236 (2012)] proposed a new algorithm to compute the upper Value-at-Risk (VaR), at a given level of confidence, of a portfolio of risky positions, whose mutual dependence is unknown. The algorithm was called Rearrangement, as it consists precisely in rearranging the columns of a matrix, whose entries are quantiles of the marginal distributions. In the following years the algorithm has performed quite well in several practical situations, but the convergence has remained an open problem. In the present paper we show that the rearrangement algorithm converges, once the deterministic procedure has been precisely defined and an initial optimality condition is satisfied.

Keywords: Value-at-Risk; Rearrangement; Ordered matrices (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-89824-7_65

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DOI: 10.1007/978-3-319-89824-7_65

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