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The Rearrangement Algorithm of Puccetti and Rüschendorf: Proving the Convergence

In: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author

Listed:
  • 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)

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.

Suggested Citation

  • Marcello Galeotti & Giovanni Rabitti & Emanuele Vannucci, 2018. "The Rearrangement Algorithm of Puccetti and Rüschendorf: Proving the Convergence," Springer Books, in: Marco Corazza & María Durbán & Aurea Grané & Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 363-367, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-89824-7_65
    DOI: 10.1007/978-3-319-89824-7_65
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