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Portfolio optimization with an envelope-based multi-objective evolutionary algorithm

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  • Branke, J.
  • Scheckenbach, B.
  • Stein, M.
  • Deb, K.
  • Schmeck, H.

Abstract

The problem of portfolio selection is a standard problem in financial engineering and has received a lot of attention in recent decades. Classical mean-variance portfolio selection aims at simultaneously maximizing the expected return of the portfolio and minimizing portfolio variance. In the case of linear constraints, the problem can be solved efficiently by parametric quadratic programming (i.e., variants of Markowitz' critical line algorithm). However, there are many real-world constraints that lead to a non-convex search space, e.g., cardinality constraints which limit the number of different assets in a portfolio, or minimum buy-in thresholds. As a consequence, the efficient approaches for the convex problem can no longer be applied, and new solutions are needed. In this paper, we propose to integrate an active set algorithm optimized for portfolio selection into a multi-objective evolutionary algorithm (MOEA). The idea is to let the MOEA come up with some convex subsets of the set of all feasible portfolios, solve a critical line algorithm for each subset, and then merge the partial solutions to form the solution of the original non-convex problem. We show that the resulting envelope-based MOEA significantly outperforms existing MOEAs.

Suggested Citation

  • Branke, J. & Scheckenbach, B. & Stein, M. & Deb, K. & Schmeck, H., 2009. "Portfolio optimization with an envelope-based multi-objective evolutionary algorithm," European Journal of Operational Research, Elsevier, vol. 199(3), pages 684-693, December.
  • Handle: RePEc:eee:ejores:v:199:y:2009:i:3:p:684-693
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    References listed on IDEAS

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    3. Schaerf, Andrea, 2002. "Local Search Techniques for Constrained Portfolio Selection Problems," Computational Economics, Springer;Society for Computational Economics, vol. 20(3), pages 177-190, December.
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    5. N. J. Jobst & M. D. Horniman & C. A. Lucas & G. Mitra, 2001. "Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 489-501.
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    Citations

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    Cited by:

    1. Babaei, Sadra & Sepehri, Mohammad Mehdi & Babaei, Edris, 2015. "Multi-objective portfolio optimization considering the dependence structure of asset returns," European Journal of Operational Research, Elsevier, vol. 244(2), pages 525-539.
    2. Ankit Dangi, 2013. "Financial Portfolio Optimization: Computationally guided agents to investigate, analyse and invest!?," Papers 1301.4194, arXiv.org.
    3. Hirschberger, Markus & Qi, Yue & Steuer, Ralph E., 2010. "Large-scale MV efficient frontier computation via a procedure of parametric quadratic programming," European Journal of Operational Research, Elsevier, vol. 204(3), pages 581-588, August.
    4. Konstantinos Anagnostopoulos & Georgios Mamanis, 2011. "Multiobjective evolutionary algorithms for complex portfolio optimization problems," Computational Management Science, Springer, vol. 8(3), pages 259-279, August.
    5. Kraft, Holger & Steffensen, Mogens, 2012. "A dynamic programming approach to constrained portfolios," CFS Working Paper Series 2012/07, Center for Financial Studies (CFS).
    6. Yu, Jing-Rung & Lee, Wen-Yi, 2011. "Portfolio rebalancing model using multiple criteria," European Journal of Operational Research, Elsevier, vol. 209(2), pages 166-175, March.
    7. Bilel JARRAYA, 2013. "Asset Allocation And Portfolio Optimization Problems With Metaheuristics: A Literature Survey," Business Excellence and Management, Faculty of Management, Academy of Economic Studies, Bucharest, Romania, vol. 3(4), pages 38-56, December.
    8. Kraft, Holger & Steffensen, Mogens, 2013. "A dynamic programming approach to constrained portfolios," European Journal of Operational Research, Elsevier, vol. 229(2), pages 453-461.
    9. Woodside-Oriakhi, M. & Lucas, C. & Beasley, J.E., 2011. "Heuristic algorithms for the cardinality constrained efficient frontier," European Journal of Operational Research, Elsevier, vol. 213(3), pages 538-550, September.
    10. Vladimir Rankovic & Mikica Drenovak & Branko Uroševic & Ranko Jelic, 2016. "Mean Univariate-GARCH VaR Portfolio Optimization: Actual Portfolio Approach," CESifo Working Paper Series 5731, CESifo Group Munich.
    11. Ranković, Vladimir & Ivanović, Miloš & Urošević, Branko & Jelic, Ranko, 2017. "Market risk management in a post-Basel II regulatory environmentAuthor-Name: Drenovak, Mikica," European Journal of Operational Research, Elsevier, vol. 257(3), pages 1030-1044.
    12. Branko Uroševic & Mikica Drenovak & Vladimir Rankovic & Ranko Jelic & Milos Ivanovic, 2016. "Market Risk Management in a Post-Basel II Regulatory Environment," CESifo Working Paper Series 6293, CESifo Group Munich.

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