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An interactive compromise programming for portfolio investment problem

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Języki publikacji
EN
Abstrakty
EN
This paper addresses an approach for solving multicriteria portfolio investment problem. The original Markowitz mean-variance model is formulated as a problem of bi-objective optimization with linear and quadratic objective functions. In the current work, this model is extended by introducing a new objective, reflecting asset properties that are useful for the portfolio allocation process. A method based on parameterized achievement scalarizing function is applied to produce Pareto optimal portfolios. A mathematical programming formulation that allows for solving the problem with conventional optimization methods is presented. In addition, a method of reflecting the decision maker’s preferences by means of changing the weights in the achievement scalarizing functions is introduced. A decision making process is simulated for the three-objective portfolio optimization problem.
Rocznik
Strony
193--210
Opis fizyczny
Bibliogr. 22 poz., rys., tab.
Twórcy
  • Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01447Warszawa, Poland
Bibliografia
  • ALCADA-ALMEIDA, L., TRALHAO, L., SANTOS, L. AND COUTINHORODRIGUES, J. (2009) A multiobjective approach to locate emergency shelters and identify evacuation routes in urban area. Geographical Analysis, 41, 9–29.
  • AOUNI, B., DOUMPOS, M., P´E REZ-GLADISH, B. AND STEUER, R. E. (2018) On the increasing importance of multiple criteria decision aid methods for portfolio selection. Journal of the Operational Research Society, 69, 1525–1542.
  • CHRISTOFIDES, N. (1975) Graph Theory. An Algorithmic Approach. Academic Press, New York.
  • EHRGOTT, M. (2000) Multicriteria Optimization. Springer, Berlin.
  • HELLWIG, Z. (1968) Zastosowanie metody taksonomicznej do typologicznego podziału krajów ze względu na poziom ich rozwoju oraz zasoby i strukturę wykwalifikowanych kadr. Przegląd Statystyczny 15 (4), 307–326. (in Polish)
  • KOLM, P. N., TÜUTÜNCÜ, R. AND FABOZZI, F.J. (2014) 60 Years of portfolio optimization: Practical challenges and current trends. European Journal of Operational Research, 234, 356–371.
  • MARKOWITZ, H.M. (1952) Portfolio selection. The Journal of Finance, 7 (1), 77–91.
  • MARKOWITZ, H.M. (1959) Portfolio Selection: Efficient Diversification of Investments. JohnWilley and Sons, New York.
  • MIETTINEN, K. (1999) Nonlinear Multiobjective Optimization. Kluwer Academic Publeshers, Boston.
  • MIETTINEN, K. AND MÄKELÄ , M. M. (2006) Synchronous approach in interactive multiobjective optimization. European Journal of Operational Research, 170, 909–922.
  • MIETTINEN, K., RUIZ, F. AND WIERZBICKI, A. P. (2009) Incorporating preference information in interactive reference point methods for multiobjective optimization. Omega, The International Journal of Management Science, 37, 450–462.
  • MONTONEN, O., RANTA, T. AND MÄKELÄ , M. M. (2019) Planning the schedule for the disposal of the spent nuclear fuel with interactive multiobjective optimization. Algorithms, 2 (12), 252.
  • NIKULIN, YU., MIETTINEN, K. AND MÄKELÄ A, M. M. (2012) A new achievement scalarizing function based on parameterization in multiobjective optimization. OR Spectrum, 34 (1), 69–87.
  • RUIZ, F., LUQUE, M., MIGUEL, F. AND DEL MAR MU˜N OZ, M. (2008) An additive achievement scalarizing function for multiobjective programming problems. European Journal of Operational Research, 188 (3), 683–694.
  • SAWARAGI, Y., NAKAYAMA, H. AND TANINO, T. (1985) Theory of Multiobjective Optimization. Academic Press, Orlando.
  • SLATER, M. (1950) Lagrange multipliers revisited. Cowles Commision Discussion Paper: Mathematics, 403.
  • STEUER, R. E. AND CHOO, E.-U. (1983) An interactive weighted Tchebyshev procedure for multiple objective programming. Mathematical Programming, 26, 326–344.
  • UTZ, S., WIMMER, M. AND STEUER, R. E. (2015) Tri-criterion modeling for constructing more-sustainable mutual funds. European Journal of Operational Research, 246, 331–338.
  • WIERZBICKI, A. P. (1980) The use of reference objectives in multiobjective optimization. In: G. Fandel and T. Gal, eds., Multiple Criteria Decision Making Theory and Applications. MCDM Theory and Applications Proceedings. Lecture Notes in Economics and Mathematical Systems 177. Springer, Berlin, 468–486.
  • WIERZBICKI, A. P. (1986) A methodological approach to comparing parametric characterizations of efficient solutions. In: G. Fandel et al., eds., Large-Scale Modelling and Interactive Decision Analysis. Lecture Notes in Economics and Mathematical Systems 273. Springer, Berlin, 27–45.
  • WIERZBICKI, A. P. (1999) Reference point approaches. In: T. Gal et al., eds., Multicriteria Decision Making: Advances in MCDM Models, Theory and Applications. Kluwer, Boston, 1–39.
  • WILPPU, O., MÄKELÄ A , M. M. AND NIKULIN, Y. (2017) New two-slope parameterized achievement scalarizing functions for nonlinear multiobjective optimization. In: N.J. Daras and T.M. Rassias, eds., Operations Research, Engineering, and Cyber Security. Springer, Berlin/Heidelberg, 113, 403–422.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-fd1ac446-06af-4e10-a7a2-63f4007b0392
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