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The paper describes the methods for constructing a quasi-efficient frontier of minimum risk portfolio under conditions of hybrid uncertainty with allowed short sales. Investor’s acceptable level of expected return is defined in crisp and fuzzy forms. Obtained results are illustrated on a model example. The dependence of the quasi-efficient frontier on the value of α-level is investigated.
Czasopismo
Rocznik
Tom
Strony
445--466
Opis fizyczny
Bibliogr. 31 poz., rys., tab.
Twórcy
autor
- Tver State University, Zhelyabova str. 33, Tver, Russia
autor
- Tver State University, Zhelyabova str. 33, Tver, Russia
autor
- Tver State University, Zhelyabova str. 33, Tver, Russia
Bibliografia
- Ammar, E. and Khalifa, H.A. (2003) Fuzzy portfolio optimization: a quadratic programming approach. Chaos, Solitons and Fractals, 18:5, 1045–1054.
- Barbaumov, V.E., Gladkikh, I.M. and Chujko, A.S. (2003) Finansovye investitsii: Uchebnik. [Financial Investments: Textbook] (in Russian), Finance and Statistics, Moscow.
- Bilbao-Terol, A., Pérez-Gladish, B., Arenas-Parra, M., Victoria, M. and Uría, R. (2006) Fuzzy compromise programming for portfolio selection. Applied Mathematics and Computation, 173:1, 251–264.
- Dubois, D. and Prade, H. (1988) Possibility Theory. Plenum Press, New York.
- Feng, Y., Hu, L. and Shu, H. (2001) The variance and covariance of fuzzy random variables and their applications. Fuzzy Sets and Systems, 120:3, 487–497, https://doi.org/10.1016/S0165-0114(99)00060-3.
- Giove, S., Funari, S. and Nardelli, C. (2006) An interval portfolio selection problem based on regret function. European Journal of Operational Research, 170:1, 253–264.
- Huang, X. (2007) Two new models for portfolio selection with stochastic returns taking fuzzy information. European Journal of Operational Research, 180:1, 396–405.
- Inuiguchi, M. and Tanino, T. (2000) Portfolio selection under independent possibilistic information. Fuzzy Sets and Systems, 115, 83–92.
- Kwakernaak, H. (1978) Fuzzy random variables. Information Science, 15, 1–29.
- Li, J., Xu, J.P. and Gen, M. (2006) A class of fuzzy random multiobjective programming problems. Mathematical and Computer Modelling, 44, 1097–1113.
- Liu, B. (2002) Theory and Practice of Uncertain Programming. Physica, Heidelberg.
- Liu, B. (2004) Uncertainty Theory: an Introduction to its Axiomatic Foundations. Springer, Berlin.
- Luhandjula, M.K. (2004) Optimisation under hybrid uncertainty. Fuzzy Sets and Systems, 146, 187–203.
- Markowitz, H. (1952) Portfolio Selection. The Journal of Finance, 7:1, 77–91, https://doi.org/10.2307/2975974.
- Markowitz, H. (1959) Portfolio Selection: Efficient Diversification of Investments. Wiley, New York.
- Nahmias, S. (1978) Fuzzy variables. Fuzzy Sets and Systems, 1, 97–110.
- Nahmias, S. (1979) Fuzzy variables in a random environment. Advances in Fuzzy Sets Theory and Applications. M.M. Gupta, R.K. Ragade and R.R. Yager, eds., NHCP, Amsterdam, 165–180.
- Parra, M.A., Terol, A.B. and Uría, M.V.R. (2001) A fuzzy goal programming approach to portfolio selection. European Journal of Operational Research, 133, 287–297.
- Soldatenko, I.S. and Yazenin, A.V. (2020) On one problem of portfolio analysis under soft constraints. Nechetkie Sistemy i Myagkie Vychisleniya. [Fuzzy Systems and Soft Computing (in Russian)], 15:1, 64–76, https://doi.org/ 10.26456/fssc71.
- Tanaka, H., Guo, P. and Turksen, I.B. (2000) Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy Sets and Systems, 111, 387–397.
- Vercher, E. (2008) Portfolios with fuzzy returns: Selection strategies based on semi-infinite programming. Journal of Computational and Applied Mathematics, 217, 381–393.
- Yazenin, A.V. (1992) Linear programming with random fuzzy data. Soviet J. Comput. Syst. Sci., 30, 86–93.
- Yazenin, A.V. (2004) Optimization with fuzzy random data and its application in financial analysis. Proceedings of International Conference on Fuzzy Sets and Soft Computing in Economics and Finance. I. Batyrshin, J. Kacprzyk, L. Sheremetov, eds. Studies in Computational Intelligence 36. Springer, Berlin Heidelberg New York.
- Yazenin, A.V. (2007) Possibilistic–Probabilistic Models and Methods of Portfolio Optimization. Perception-based Data Mining and Decision Making in Economics and Finance, Studies in Computational Intelligence. I. Batyrshin, J. Kacprzyk, L. Sheremetov, L.A. Zadeh, eds. Springer, Berlin, Heidelberg, 241–259, https://doi.org/10.1007/978-3-540-36247-0 9.
- Yazenin, A.V. (2016) Osnovnye ponyatiya teorii vozmozhnostej. Matematicheskij apparat dlya prinyatiya reshenij v usloviyakh gibridnoj neopredelennosti [Basic concepts of the theory of possibilities. Mathematical decisionmaking apparatus in a hybrid uncertainty] (in Russian). Fizmatlit Publ., Moscow.
- Yazenin, A. and Soldatenko, I. (2018) A portfolio of minimum risk in a hybrid uncertainty of a possibilistic-probabilistic type: comparative study. Advances in Fuzzy Logic and Technology 2017. 643 (EUSFLAT 2017, IWIFSGN 2017), Advances in Intelligent Systems and Computing, J. Kacprzyk, E. Szmidt, S. Zadrozny, K. Atanassov and M. Krawczak, eds., 551–563, https://doi.org/10.1007/978-3-319-66827-7 51.
- Yazenin, A.V. and Soldatenko, I.S. (2021) Model of a minimal risk portfolio under hybrid uncertainty. Control and Cybernetics, 50:2, 315–332.
- Yazenin, A.V. and Wagenknecht, M. (1996) Possibilistic Optimization. A measure-based approach. Aktuelle Reihe 6/96, Brandenburgische Technische Universitat, Cottbus, Germany.
- Zadeh, L.A. (1965) Fuzzy sets. Information and Control, 8, 338–353.
- Zadeh, L.A. (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3–28.
- Zhang, W.G. and Nie, Z.K. (2004) On admissible efficient portfolio selection problem. Applied Mathematics and Computation, 159, 357–371.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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