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Multiple criteria linear programming model for portfolio selection


  • Włodzimierz Ogryczak


The portfolio selection problem is usually considered as a bicriteria optimization problem where a reasonable trade-off between expected rate of return and risk is sought. In the classical Markowitz model the risk is measured with variance, thus generating a quadratic programming model. The Markowitz model is frequently criticized as not consistent with axiomatic models of preferences for choice under risk. Models consistent with the preference axioms are based on the relation of stochastic dominance or on expected utility theory. The former is quite easy to implement for pairwise comparisons of given portfolios whereas it does not offer any computational tool to analyze the portfolio selection problem. The latter, when used for the portfolio selection problem, is restrictive in modeling preferences of investors. In this paper, a multiple criteria linear programming model of the portfolio selection problem is developed. The model is based on the preference axioms for choice under risk. Nevertheless, it allows one to employ the standard multiple criteria procedures to analyze the portfolio selection problem. It is shown that the classical mean-risk approaches resulting in linear programming models correspond to specific solution techniques applied to our multiple criteria model. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • Włodzimierz Ogryczak, 2000. "Multiple criteria linear programming model for portfolio selection," Annals of Operations Research, Springer, vol. 97(1), pages 143-162, December.
  • Handle: RePEc:spr:annopr:v:97:y:2000:i:1:p:143-162:10.1023/a:1018980308807
    DOI: 10.1023/A:1018980308807

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    Cited by:

    1. Constantin Zopounidis & Michael Doumpos, 2013. "Multicriteria decision systems for financial problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 241-261, July.
    2. repec:spr:annopr:v:242:y:2016:i:2:d:10.1007_s10479-013-1435-z is not listed on IDEAS
    3. Panagiotis Xidonas & George Mavrotas & John Psarras, 2010. "Equity portfolio construction and selection using multiobjective mathematical programming," Journal of Global Optimization, Springer, vol. 47(2), pages 185-209, June.
    4. Hirschberger, Markus & Qi, Yue & Steuer, Ralph E., 2007. "Randomly generating portfolio-selection covariance matrices with specified distributional characteristics," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1610-1625, March.
    5. repec:pal:jorsoc:v:61:y:2010:i:8:d:10.1057_jors.2009.74 is not listed on IDEAS
    6. Polak, George G. & Rogers, David F. & Sweeney, Dennis J., 2010. "Risk management strategies via minimax portfolio optimization," European Journal of Operational Research, Elsevier, vol. 207(1), pages 409-419, November.
    7. repec:eee:ejores:v:265:y:2018:i:2:p:655-672 is not listed on IDEAS
    8. Rafael Rodríguez & Mariano Luque & Mercedes González, 2011. "Portfolio selection in the Spanish stock market by interactive multiobjective programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 213-231, July.
    9. repec:spr:annopr:v:267:y:2018:i:1:d:10.1007_s10479-016-2346-6 is not listed on IDEAS
    10. TKACENKO, Alexandra, 2014. "Linear Programming Methods For Solving The Portfolio’S Problems," Journal of Financial and Monetary Economics, Centre of Financial and Monetary Research "Victor Slavescu", vol. 1(1), pages 216-221.
    11. Klamroth, Kathrin & Köbis, Elisabeth & Schöbel, Anita & Tammer, Christiane, 2017. "A unified approach to uncertain optimization," European Journal of Operational Research, Elsevier, vol. 260(2), pages 403-420.
    12. repec:spr:mathme:v:86:y:2017:i:3:d:10.1007_s00186-017-0613-1 is not listed on IDEAS
    13. Mut, Murat & Wiecek, Margaret M., 2011. "Generalized equitable preference in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 212(3), pages 535-551, August.
    14. repec:spr:annopr:v:262:y:2018:i:2:d:10.1007_s10479-016-2137-0 is not listed on IDEAS
    15. repec:spr:annopr:v:247:y:2016:i:2:d:10.1007_s10479-015-1947-9 is not listed on IDEAS


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