Using Fuzzy Possibilistic Mean and Variance in Portfolio Selection Model.
ABSTRACT There are many non-probabilistic factors that affect the financial markets such that the returns of risky assets may be regarded
as fuzzy numbers. This paper discusses the portfolio selection problem based on the possibilistic mean and variance of fuzzy
numbers, which can better described an uncertain environment with vagueness and ambiguity to compare with conventional probabilistic
mean-variance methodology. Markowitz’s mean-variance model is simplified a linear programming when returns of assets are symmetric
triangular fuzzy numbers, so the possibilistic efficient portfolios can be easily obtained by some related algorithms.
- European Journal of Operational Research 02/1986; 23(3):294-300. · 2.04 Impact Factor
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ABSTRACT: This paper develops a closed form solution of the mean-variance portfolio selection problem for uncorrelated and bounded assets when an additional technical assumption is satisfied. Although the assumption of uncorrelated assets is unduly restrictive, the explicit determination of the efficient asset holdings in the presence of bound constraints gives insight into the nature of the efficient frontier. The mean-variance portfolio selection problem considered here deals with the budget constraint and lower bounds or the budget constraint and upper bounds. For the mean-variance portfolio selection problem dealing with lower bounds the closed form solution is derived for two cases: a universe of only risky assets and a universe of risky assets plus an additional asset which is risk free. For the mean-variance portfolio selection problem dealing with upper bounds, the results presented are for a universe consisting only of risky assets. In each case, the order in which the assets are driven to their bounds depends on the ordering of their expected returns.Mathematical Methods of Operational Research 10/2000; 52(2):195-212. · 0.31 Impact Factor
Book: Fuzzy sets01/1987; Narodna prosveta.