Fuzzy cross-entropy, mean, variance, skewness models for portfolio selection

In this paper, fuzzy stock portfolio selection models that maximize mean and skewness as well as minimize portfolio variance and cross-entropy are proposed. Because returns are typically asymmetric, in addition to typical mean and variance considerations, third order moment skewness is also considered in generating a larger payoff. Cross-entropy is used to quantify the level of discrimination in a return for a given satisfactory return value. As returns are uncertain, stock returns are considered triangular fuzzy numbers. Stock price data from the Bombay Stock Exchange are used to illustrate the effectiveness of the proposed model. The solutions are done by genetic algorithms.