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Order υ Entropy and Cross Entropy of Uncertain Variables for Portfolio Selection
Alireza Sajedi,Gholamhossein Yari 한국지능시스템학회 2020 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.20 No.1
In this study, we proposed definition of order υ entropy and order υ cross entropy of uncertain variables under uncertainty theory. Moreover, order υ entropy and order υ cross entropy of uncertain variables were applied to mean-variance portfolio selection model. We also attempted to examine the applications of these measures with different order υ values. The effect of the υ in order υ entropy and cross entropy on portfolio selection were considered using the order υ entropy-mean-variance and 571781799order υ entropy-mean-variance presented models. As a result of this approach, by using different values of υ, diversity of asset allocations could be achieved.
Seyyed Hamed Abtahi,Gholamhossein Yari,Farhad Hosseinzadeh Lotfi,Rahman Farnoosh 한국지능시스템학회 2021 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.21 No.1
Empirical studies illustrate that in numerous cases the returns of securities are not normally distributed. In this paper, skew-normal uncertainty distribution is proposed to capture skewness in the portfolio selection problem. Furthermore, the concept of asymmetric entropy for uncertain variables as the quantifier of diversification is presented and its mathematical properties such as translation invariance and positive linearity are studied. To examine the effect of asymmetric entropy parameter on portfolio diversification, a mean-CVaR-entropy portfolio selection problem is presented based on asymmetric entropy with different parameter values and logarithm entropy. A non-dominated sorting genetic algorithm II (NSGA-II) is implemented in MATLAB to solve the corresponding problem. Numerical results show that asymmetric entropy for a specific parameter value will outperform logarithm entropy in portfolio diversification.