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A clustering approach for scenario tree reduction: an application to a stochastic programming portfolio optimization problem

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  • Patrizia Beraldi
  • Maria Bruni

Abstract

This paper deals with the problem of scenario tree reduction for stochastic programming problems. In particular, a reduction method based on cluster analysis is proposed and tested on a portfolio optimization problem. Extensive computational experiments were carried out to evaluate the performance of the proposed approach, both in terms of computational efficiency and efficacy. The analysis of the results shows that the clustering approach exhibits good performance also when compared with other reduction approaches. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Patrizia Beraldi & Maria Bruni, 2014. "A clustering approach for scenario tree reduction: an application to a stochastic programming portfolio optimization problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 934-949, October.
    • Handle: RePEc:spr:topjnl:v:22:y:2014:i:3:p:934-949
    DOI: 10.1007/s11750-013-0305-9
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    References listed on IDEAS

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    1. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    2. Gulpinar, Nalan & Rustem, Berc & Settergren, Reuben, 2004. "Simulation and optimization approaches to scenario tree generation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1291-1315, April.
    3. Geyer, Alois & Hanke, Michael & Weissensteiner, Alex, 2010. "No-arbitrage conditions, scenario trees, and multi-asset financial optimization," European Journal of Operational Research, Elsevier, vol. 206(3), pages 609-613, November.
    4. René Henrion & Christian Küchler & Werner Römisch, 2009. "Scenario reduction in stochastic programming with respect to discrepancy distances," Computational Optimization and Applications, Springer, vol. 43(1), pages 67-93, May.
    5. Jitka Dupačová & Giorgio Consigli & Stein Wallace, 2000. "Scenarios for Multistage Stochastic Programs," Annals of Operations Research, Springer, vol. 100(1), pages 25-53, December.
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    Cited by:

    1. Weiguo Zhang & Xiaolei He, 2022. "A New Scenario Reduction Method Based on Higher-Order Moments," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 1903-1918, July.
    2. P. Beraldi & M. E. Bruni, 2020. "Efficiency evaluation under uncertainty: a stochastic DEA approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 519-538, December.
    3. Markéta Horejšová & Sebastiano Vitali & Miloš Kopa & Vittorio Moriggia, 2020. "Evaluation of scenario reduction algorithms with nested distance," Computational Management Science, Springer, vol. 17(2), pages 241-275, June.
    4. Justo Puerto & Moises Rodr'iguez-Madrena & Andrea Scozzari, 2019. "Location and portfolio selection problems: A unified framework," Papers 1907.07101, arXiv.org.
    5. Florian Ziel, 2020. "The energy distance for ensemble and scenario reduction," Papers 2005.14670, arXiv.org, revised Oct 2020.

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