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A Linear Programming Formulation of the General Portfolio Selection Problem†

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  • Stone, Bernell K.

Abstract

Almost two decades ago, Markowitz [12] formulated the portfolio selection problem as a parametric quadratic programming problem. The crux of his formulation was the mean-variance assumption which asserted that a portfolio is efficient if (and only if): (1) it has less variance than any other feasible portfolio with the same return and (2) it has more return than any other feasible portfolio with the same variance.

Suggested Citation

  • Stone, Bernell K., 1973. "A Linear Programming Formulation of the General Portfolio Selection Problem†," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(4), pages 621-636, September.
    • Handle: RePEc:cup:jfinqa:v:8:y:1973:i:04:p:621-636_01
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    Cited by:

    1. Li, Han-Lin & Tsai, Jung-Fa, 2008. "A distributed computation algorithm for solving portfolio problems with integer variables," European Journal of Operational Research, Elsevier, vol. 186(2), pages 882-891, April.
    2. Justin Dzuche & Christian Deffo Tassak & Jules Sadefo Kamdem & Louis Aimé Fono, 2021. "On two dominances of fuzzy variables based on a parametrized fuzzy measure and application to portfolio selection with fuzzy return," Annals of Operations Research, Springer, vol. 300(2), pages 355-368, May.
    3. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    4. John B. Guerard, Jr. & Robert A. Gillam & Harry Markowitz & Ganlin Xu & Shijie Deng & Ziwei (Elaine) Wang, 2018. "Data Mining Corrections Testing in Chinese Stocks," Interfaces, INFORMS, vol. 48(2), pages 108-120, April.
    5. 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.
    6. Ralph Steuer & Yue Qi & Markus Hirschberger, 2007. "Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection," Annals of Operations Research, Springer, vol. 152(1), pages 297-317, July.
    7. P Xidonas & G Mavrotas & J Psarras, 2010. "A multiple criteria decision-making approach for the selection of stocks," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(8), pages 1273-1287, August.
    8. Justin Dzuche & Christian Deffo Tassak & Jules Sadefo-Kamdem & Louis Aimé Fono, 2019. "On Two Dominances of Fuzzy Variables based on a Parametric Fuzzy Measure and Application to Portfolio Selection with Fuzzy Return," Working Papers hal-02433438, HAL.
    9. Esther Mohr & Robert Dochow, 2017. "Risk management strategies for finding universal portfolios," Annals of Operations Research, Springer, vol. 256(1), pages 129-147, September.
    10. Nagurney, Anna & Ke, Ke, 2006. "Financial networks with intermediation: Risk management with variable weights," European Journal of Operational Research, Elsevier, vol. 172(1), pages 40-63, July.
    11. Bai, Zhidong & Liu, Huixia & Wong, Wing-Keung, 2016. "Making Markowitz's Portfolio Optimization Theory Practically Useful," MPRA Paper 74360, University Library of Munich, Germany.
    12. Yue Qi & Ralph E. Steuer & Maximilian Wimmer, 2017. "An analytical derivation of the efficient surface in portfolio selection with three criteria," Annals of Operations Research, Springer, vol. 251(1), pages 161-177, April.
    13. Florian Methling & Rüdiger Nitzsch, 2019. "Thematic portfolio optimization: challenging the core satellite approach," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 33(2), pages 133-154, June.
    14. Martin R. Young, 1998. "A Minimax Portfolio Selection Rule with Linear Programming Solution," Management Science, INFORMS, vol. 44(5), pages 673-683, May.
    15. Mansini, Renata & Speranza, Maria Grazia, 1999. "Heuristic algorithms for the portfolio selection problem with minimum transaction lots," European Journal of Operational Research, Elsevier, vol. 114(2), pages 219-233, April.
    16. 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.
    17. Li, Xiang & Qin, Zhongfeng & Kar, Samarjit, 2010. "Mean-variance-skewness model for portfolio selection with fuzzy returns," European Journal of Operational Research, Elsevier, vol. 202(1), pages 239-247, April.
    18. Arenas Parra, M. & Bilbao Terol, A. & Rodriguez Uria, M. V., 2001. "A fuzzy goal programming approach to portfolio selection," European Journal of Operational Research, Elsevier, vol. 133(2), pages 287-297, January.
    19. Heuts, R.M.J., 1978. "Portfolio models and time series analysis," Other publications TiSEM 48458631-edc8-42e9-8359-4, Tilburg University, School of Economics and Management.
    20. Amritansu Ray & Sanat Kumar Majumder, 2018. "Multi objective mean–variance–skewness model with Burg’s entropy and fuzzy return for portfolio optimization," OPSEARCH, Springer;Operational Research Society of India, vol. 55(1), pages 107-133, March.
    21. Zhihui Lv & Amanda M. Y. Chu & Wing Keung Wong & Thomas C. Chiang, 2021. "The maximum-return-and-minimum-volatility effect: evidence from choosing risky and riskless assets to form a portfolio," Risk Management, Palgrave Macmillan, vol. 23(1), pages 97-122, June.

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