Portfolio Selection in the Presence of Multiple Criteria

  • Ralph E. Steuer
  • Yue Qi
  • Markus Hirschberger
Part of the Springer Optimization and Its Applications book series (SOIA, volume 18)


Multiple Criterion Stochastic Program Portfolio Optimization Portfolio Selection Portfolio Return 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aouni, B., Ben Abdelaziz, F., and El-Fayedh, R. Chance constrained compromise programming for portfolio selection. Laboratoire LARODEC, Institut Superieur de Gestion, La Bardo 2000, Tunis, Tunisia, 2006.Google Scholar
  2. 2.
    Arenas Parra, M., Bilbao Terol, A., and Rodríguez Uría, M. V. A fuzzy goal programming approach to portfolio selection. European Journal of Operational Research, 133(2):287–297, 2001.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Ballestero, E. Using compromise programming in a stock market pricing model. In Y. Y. Haimes and R. E. Steuer, Editors, Lecture Notes in Economics and Mathematical Systems, vol. 487. Springer-Verlag, Berlin, 2002, pages 388–399.Google Scholar
  4. 4.
    Ballestero, E., and Plà-Santamaría, D. Selecting portfolios for mutual funds. Omega, 32:385–394, 2004.CrossRefGoogle Scholar
  5. 5.
    Ballestero, E., and Romero, C. Portfolio selection: A compromise programming solution. Journal of the Operational Research Society, 47(11):1377–1386, 1996.MATHGoogle Scholar
  6. 6.
    Bana e Costa, C. A., and Soares, J. O. Multicriteria approaches for portfolio selection: An overview. Review of Financial Markets, 4(1):19–26, 2001.Google Scholar
  7. 7.
    Bana e Costa, C. A., and Soares, J. O. A multicriteria model for portfolio management. European Journal of Finance, 10(3):198–211, 2004.CrossRefGoogle Scholar
  8. 8.
    Bernoulli, D. Specimen theoria novae de mensura sortis. Commentarii Academiae Scientarum Imperialis Petropolitnae, 5(2):175–192, 1738. Translated into English by L. Sommer, Exposition of a new theory on the measurement of risk, Econometrica, 22(1):23–26, 1954.MathSciNetGoogle Scholar
  9. 9.
    Best, M. J. An algorithm for the solution of the parametric quadratic programming problem. In B. Riedmüller H. Fischer and S. Schäffler, Editors, Applied Mathematics and Parallel Computing: Festschrift for Klaus Ritter. Physica-Verlag, Berlin, 1996, pages 57–76.Google Scholar
  10. 10.
    Best, M. J., and Hlouskova, J. An algorithm for portfolio optimization with transaction costs. Management Science, 51(11):1676–1688, 2005.CrossRefGoogle Scholar
  11. 11.
    Best, M.J., and Kale, J. Quadratic programming for large-scale portfolio optimization. In J. Keyes, Editor, Financial Services Information Systems. CRC Press, Boca Raton, FL, 2000, pages 513–529.Google Scholar
  12. 12.
    Bouri, G., Martel, J. M., and Chabchoub, H. A multi-criterion approach for selecting attractive portfolio. Journal of Multi-Criteria Decision Analysis, 11(3):269–277, 2002MATHCrossRefGoogle Scholar
  13. 13.
    Caballero, R., Cerdá, E., Muñoz, M. M., Rey, L., and Stancu-Minasian, I. M. Efficient solution concepts and their relations in stochastic multiobjective programming. Journal of Optimization Theory and Applications, 110(1):53–74, 2001MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Campbell, J. Y., Lo, A. W., and Mackinlay, A. C. The Econometrics of Financial Markets. Princeton University Press, Princeton, NJ, 1997.Google Scholar
  15. 15.
    Chow, G. Portfolio selection based on return, risk, and relative performance. Financial Analysts Journal, 54–60, March–April 1995.Google Scholar
  16. 16.
    Chunhachinda, P., Dandapani, K., Hamid, S., and Prakash, A. J. Portfolio selection and skewness evidence from international stock markets. Journal of Banking & Finance, 21:143–167, 1997.CrossRefGoogle Scholar
  17. 17.
    Colson, G., and DeBruyn, C. An integrated multiobjective portfolio management system. Mathematical and Computer Modelling, 12(10–11):1359–1381, 1989CrossRefGoogle Scholar
  18. 18.
    Deb, K. Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley, New York, 2001.Google Scholar
  19. 19.
    Dominiak, C. An application of interactive multiple objective goal programming on the Warsaw stock exchange. In R. Caballero, F. Ruiz, and R. E. Steuer, Editors, Lecture Notes in Economics and Mathematical Systems, vol. 455. Springer-Verlag, Berlin, 1997a, pages 66–74.Google Scholar
  20. 20.
    Dominiak, C. Portfolio selection using the idea of reference solution. In G. Fandel and T. Gal, Editors, Lecture Notes in Economics and Mathematical Systems, vol. 448. Springer-Verlag, Berlin, 1997b, pages 593–602.Google Scholar
  21. 21.
    Doumpos, M., Spanos, M., and Zopounidis, C. On the use of goal programming techniques in the assessment of financial risks. Journal of Euro-Asian Management, 5(1):83–100, 1999.Google Scholar
  22. 22.
    Ehrgott, M., Klamroth, K., and Schwehm, C. An MCDM approach to portfolio optimization. European Journal of Operational Research, 155(3):752–770, 2004.MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Elton, E. J., Gruber, M. J., Brown, S. J., and Goetzmann, W. Modern Portfolio Theory and Investment Analysis, 6th edition. John Wiley, New York, 2002.Google Scholar
  24. 24.
    Fliege, J. Gap-free computation of Pareto-points by quadratic scalarizations. Mathematical Methods of Operations Research, 59(1):69–89, 2004MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Hallerbach, W. G., and Spronk, J. A multidimensional framework for financial-economic decisions. Journal of Multi-Criteria Decision Analysis, 11(3):111–124, 2002a.MATHCrossRefGoogle Scholar
  26. 26.
    Hallerbach, W.G., and Spronk, J. The relevance of MCDM for financial decisions. Journal of Multi-Criteria Decision Analysis, 11(4–5):187–195, 2002b.MATHCrossRefGoogle Scholar
  27. 27.
    Hirschberger, M., Qi, Y., and Steuer, R. E. Tri-criterion quadratic-linear programming. Working paper, Department of Banking and Finance, University of Georgia, Athens, 2007.Google Scholar
  28. 28.
    Hurson, C., and Zopounidis, C. On the use of multi-criteria decision aid methods to portfolio selection. Journal of Euro-Asian Management, 1(2):69–94, 1995.Google Scholar
  29. 29.
    IBM 1401 Portfolio Selection Program (1401-F1-04X) Program Reference Manual. IBM, New York, 1965.Google Scholar
  30. 30.
    Kliber, P. A three-criteria portfolio selection: Mean return, risk and costs of adjustment. Akademia Ekonomiczna w Poznaniu, Poznan, Poland, 2005.Google Scholar
  31. 31.
    Konno, H., and Suzuki, K.-I. A mean-variance-skewness portfolio optimization model. Journal of the Operations Research Society of Japan, 38(2):173–187, 1995.MATHGoogle Scholar
  32. 32.
    Konno, H., Shirakawa, H., and Yamazaki, H. A mean-absolute deviation-skewness portfolio optimization model. Annals of Operations Research, 45:205–220, 1993.MATHCrossRefMathSciNetGoogle Scholar
  33. 33.
    Korhonen, P., and Karaivanova, J. An algoithm for projecting a reference direction onto the nondominated set of given points. IEEE Transactions on Systems, Man, and Cybernetics, 29(5):429–435, 1999.CrossRefGoogle Scholar
  34. 34.
    Korhonen, P., and Wallenius, J. A Pareto race. Naval Research Logistics, 35(6):615–623, 1988.MATHCrossRefGoogle Scholar
  35. 35.
    Korhonen, P., and Yu, G.-Y. A reference direction approach to multiple objective quadratic-linear programming. European Journal of Operational Research, 102(3):601–610, 1997MATHCrossRefGoogle Scholar
  36. 36.
    Lee, S. M., and Lerro, A. J. Optimizing the portfolio selection for mutual funds. Journal of Finance, 28(5):1087–1101, 1973.CrossRefGoogle Scholar
  37. 37.
    L(Hoir, H., and Teghem, J. Portfolio selection by MOLP using interactive branch and bound. Foundations of Computing and Decision Sciences, 20(3):175–185, 1995Google Scholar
  38. 38.
    Lo, A. W., Petrov, C., and Wierzbicki, M. It(s 11pm - Do you know where your liquidity is? The mean-variance-liquidity frontier. Journal of Investment Management, 1(1):55–93, 2003.Google Scholar
  39. 39.
    Lotov, A.B., Bushenkov, V.A., and Kamenev, G.K. Interactuve Decision Maps: Approximation and Visualization of Pareto Frontier. Kluwer Academic Publishers, Boston, 2004.Google Scholar
  40. 40.
    Markowitz, H. M. Portfolio selection. Journal of Finance, 7(1):77–91, 1952.CrossRefGoogle Scholar
  41. 41.
    Markowitz, H. M. The optimization of a quadratic function subject to linear constraints. Naval Research Logistics Quarterly, 3:111–133, 1956.CrossRefMathSciNetGoogle Scholar
  42. 42.
    Markowitz, H. M. The early history of portfolio selection: 1600–1960. Financial Analysts Journal, 5–16, July 1999.Google Scholar
  43. 43.
    Markowitz, H.M., and Perold, A. Portfolio analysis with factors and scenarios. Journal of Finance, 36(14):871–877, 1981a.CrossRefGoogle Scholar
  44. 44.
    Markowitz, H. M., and Perold, A. Sparsity and piecewise linearity in large scale portfolio optimization problems. In I. Duff, Editor, Sparse Matrices and Their Use (The Institute of Mathematics and Its Applications Conference Series). Academic Press, New York, 1981b, pages 89–108.Google Scholar
  45. 45.
    Markowitz, H. M., and Todd, G. P. Mean-Variance Analysis in Portfolio Choice and Capital Markets. Frank J. Fabozzi Associates, New Hope, PA, 2000.Google Scholar
  46. 46.
    Miettinen, K. M. Nonlinear Multiobjective Optimization. Kluwer, Boston, 1999.Google Scholar
  47. 47.
    Mitra, G., Kyriakis, T., Lucas, C., and Pirbhai, M. A review of portfolio planning: models and systems. In S. E. Satchell and A. E. Scowcroft, Editors, Advances in Portfolio Construction and Implementation. Butterworth-Heinemann, Oxford, 2003, pages 1–39.Google Scholar
  48. 48.
    Ogryczak, W. Multiple criteria linear programming model for portfolio selection. Annals of Operations Research, 97:143–162, 2000.MATHCrossRefMathSciNetGoogle Scholar
  49. 49.
    Pardalos, P. M., Sandström, M., and Zopounidis, C. On the use of optimization models for portfolio selection: A review and some computational results. Computational Economics, 7(4):227–244, 1994.MATHCrossRefMathSciNetGoogle Scholar
  50. 50.
    Perold, A. Large-scale portfolio optimization. Management Science, 30(10):1143–1160, 1984.MATHCrossRefMathSciNetGoogle Scholar
  51. 51.
    Prakash, A. J., Chang, C. H., and Pactwa, T. E. Selecting a portfolio with skewness: Recent evidence from US, European, and Latin American equity markets. Journal of Banking & Finance, 27:1375–1390, 2003.CrossRefGoogle Scholar
  52. 52.
    Prékopa, A. Stochastic Programming. Kluwer Academic Publishers, Dordrecht, 1995.Google Scholar
  53. 53.
    Roy, A. D. Safety first and the holding of assets. Econometrica, 20(3):431–449, 1952.MATHCrossRefGoogle Scholar
  54. 54.
    Saaty, T. L. Decision Making for Leaders. RWS Publications, Pittsburgh, 1999.Google Scholar
  55. 55.
    Slowinski, R., and Teghem, J., Editors Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming Under Uncertaintyd. Kluwer Academic Publishers, Dordrecht, 1990.Google Scholar
  56. 56.
    Spronk, J. Interactive Multiple Goal Programming: Applications to Financial Management. Martinus Nijhoff Publishing, Boston, 1981.Google Scholar
  57. 57.
    Spronk, J., and Hallerbach, W.G. Financial modelling: Where to go? With an illustration for portfolio management. European Journal of Operational Research, 99(1):113–127, 1997.MATHCrossRefGoogle Scholar
  58. 58.
    Spronk, J., Steuer, R. E., and Zopounidis, C. Multicriteria decision analysis/aid in finance. In J. Figuiera, S. Greco, and M. Ehrgott, Editors, Multiple Criteria Decision Analysis: State of the Art Surveys. Springer Science, New York, 2005, pages 799–857.Google Scholar
  59. 59.
    Stancu-Minasian, I. Stochastic Programming with Multiple-Objective Functions. D. Reidel Publishing Company, Dordrecht, 1984.Google Scholar
  60. 60.
    Steuer, R. E., and Na, P. Multiple criteria decision making combined with finance: A categorized bibliography. European Journal of Operational Research, 150(3):496–515, 2003MATHCrossRefGoogle Scholar
  61. 61.
    Steuer, R. E., Qi, Y., and Hirschberger, M. Multiple objectives in portfolio selection. Journal of Financial Decision Making, 1(1):5–20, 2005.Google Scholar
  62. 62.
    Steuer, R. E., Qi, Y., and Hirschberger, M. Developments in multi-attribute portfolio selection. In T. Trzaskalik, Editor, Multiple Criteria Decision Making (05. Karol Adamiecki University of Economics in Katowice, 2006a, pages 251–262.Google Scholar
  63. 63.
    Steuer, R. E., Qi, Y., and Hirschberger, M. Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection. Annals of Operations Research, 2006b. forthcoming.Google Scholar
  64. 64.
    Steuer, R. E., Silverman, J., and Whisman, A. W. A combined Tchebycheff/aspiration criterion vector interactive multiobjective programming procedure. Management Science, 39(10):1255–1260, 1993.MATHCrossRefGoogle Scholar
  65. 65.
    Stone, B. K. A linear programming formulation of the general portfolio selection problem. Journal of Financial and Quantitative Analysis, 8(4):621–636, 1973CrossRefGoogle Scholar
  66. 66.
    Tamiz, M., Hasham, R., Jones, D. F., Hesni, B., and Fargher, E. K. A two staged goal programming model for portfolio selection. In M. Tamiz, Editor, Lecture Notes in Economics and Mathematical Systems vol. 432. Springer-Verlag, Berlin, 1996, pages 386–399.Google Scholar
  67. 67.
    Von Neumann, J., and Morgenstern, O. Theory of Games and Economic Behavior. 2nd Edition, Princeton, NJ, 1947.Google Scholar
  68. 68.
    Xu, J., and Li, J. A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model. Journal of Computational and Applied Mathematics, 146:99–113, 2002MATHCrossRefMathSciNetGoogle Scholar
  69. 69.
    Yu, G. Y. A multiple criteria approach to choosing an efficient stock portfolio at the Helsinki stock exchange. Journal of Euro-Asian Management, 3(2):53–85, 1997.Google Scholar
  70. 70.
    Ziemba, W. T. The Stochastic Programming Approach to Asset, Liability, and Wealth Management. Research Foundation of the AIMR, Charlottesville, VA, 2003.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Terry College of BusinessUniversity of GeorgiaAthensUSA
  2. 2.Hedge Fund Research InstituteInternational University of MonacoPrincipality of MonacoMonaco
  3. 3.Department of MathematicsUniversity of Eichstätt-IngolstadtEichstättGermany

Personalised recommendations