Weighted portfolio selection models based on possibility theory
Tóm tắt
In this paper, we discuss portfolio selection problem in a fuzzy uncertain environment. Based on the Fullér’s and Zhang’s notations, we discuss some properties of weighted lower and upper possibilistic means and variances as in probability theory. We further present two weighted possibilistic portfolio selection models with bounded constraint, which can be transformed to linear programming problems under the assumption that the returns of assets are trapezoidal fuzzy numbers. At last, a numerical example is given to illustrate our proposed effective means and approaches.
Tài liệu tham khảo
Markowitz H (1952) Portfolio selection. Journal of Finance 7:77–91
Markowitz H (1959) Portfolio selection: Efficient Diversification of Investments. Wiley, New York
Sharpe WF (1970) Portfolio theory and capital markets. McGraw-Hill, New York
Merton RC (1972) An analytic derivation of the efficient frontier. Journal of Finance and Quantitative Analysis 7:1851–1872
Perold AF (1984) Large-scale portfolio optimization. Management Science 30:1143–1160
Vörös J (1986) Portfolio analysis-An analytic derivation of the efficient portfolio frontier. European Journal of Operational Research 23:294–300
Sheen JN (2005) Fuzzy financial profitability analyses of demand side management alternatives from participant perspective. Information Sciences 169:329–364
Zadeh LA (1965) Fuzzy set. Information and Control 8:338–353
Watada J (1997) Fuzzy portfolio selection and its applications to decision making. Tatra Mountains Mathematical Publication 13:219–248
Inuiguchi M, Tanino T (2000) Portfolio selection under independent possibilistic information. Fuzzy Sets and Systems 115:83–92
Wang SY, Zhu SS (2002) On fuzzy portfolio selection problem. Fuzzy Optimization and Decision Making 1:361–377
Ramaswamy S (1998) Portfolio selection using fuzzy decision theory. Working Paper of Bank for International Settlements 59
Tanaka H, Guo P (1999) Portfolio selection based on upper and lower exponential possibility distributions. European Journal of Operational Research 114:115–126
Tanaka H, Guo P, Türksen IB (2000) Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy sets and systems 111:387–397
Carlsson C, Fullér R (2001) On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems 122:315–326
Carlsson C, Fullér R, Majlender P (2002) A possibilistic approach to selecting portfolios with highest utility score. Fuzzy Sets and Systems 131:13–21
Ammar EE (2008) On fuzzy random multiobjective quadratic programming. European Journal of Operational Research 193:329–341
Arenas Parra M, Bilbao Terol A, Rodriguez Uria MV (2001) A fuzzy goal programming approach to portfolio Selection. European Journal of Oprational Research 133:287–297
Bilbao Terol A, Perez Gladish B, Arenas Parra M, Rodriguez Uria MV (2006) Fuzzy compromise programming for portfolio selection. Applied Mathematics and Computation 173: 251–264
Deng XT, Li ZF, Wang SY (2005) A minimax portfolio selection strategy with equilibrium. European Journal of Operational Research 166:278–292
Gupta P, Mehlawat MK, Saxena A (2008) Asset portfolio optimization using fuzzy mathematical programming. Information Sciences 178:1734–1755
Lacagnina V, Pecorella A (2006) A stochastic soft constraints fuzzy model for a portfolio selection problem. Fuzzy Sets and Systems 157:1317–1327
Huang X (2007) Two new models for portfolio selection with stochastic returns taking fuzzy information. European Journal of Operational Research 180: 396–405
Huang X (2008) Expected model for portfolio selection with random fuzzy returns. International Journal of General Systems 37:319–328
Huang X (2008) Mean-semivariance models for fuzzy portfolio selection. Journal of Computational and Applied Mathematics 217:1–8
Huang X (2008) Portfolio selection with a new definition of risk. European Journal of Operational Research 186:351–357
Zhang WG (2007) Possibilistic Mean-Standard Deviation Models to Portfolio Selection for Bounded Assets. Applied Mathematics and Computation 189:1614–1623
Zhang WG, Wang YL, Chen ZP, Nie ZK (2007) Possibilistic mean-variance models and efficient frontiers for portfolio selection problem. Information Sciences 177(13): 2787–2801
Zhang WG, Xiao WL, Wang YL (2009) A fuzzy portfolio selection method based on possibilistic mean and variance. Soft Computing 13:627–633
Zhang WG, Nie ZK (2003) On possibilistic variance of fuzzy numbers. Lecture Notes in Artificial Intelligence 2639:398–402
Chen W, Zhang R, Zhang WG, Cai YM (2007) A fuzzy portfolio selection methodology under investing constraints, Proceedings of the Second International Conference of Fuzzy Information and Engineering (ICFIE) 564–572
Fullér R, Majlender P (2003) On weighted possibilistic mean and variance of fuzzy numbers. Fuzzy Sets and Systems 136:363–374
Zhang WG, Xiao WL (2009) On weighted lower and upper possibilistic means and variances of fuzzy numbers and its application in decision. Knowledge and Information System 18:311–330
Dubois D, Prade H (1988) Possibility Theory, Plenum Press, New York