Diversified models for portfolio selection based on uncertain semivariance

Since the financial markets are complex, sometimes the future security returns are represented mainly based on experts estimations due to lack of historical data. This paper proposes a semivariance method for diversified portfolio selection, in which the security returns are given subjective to experts estimations and depicted as uncertain variables. In the paper, three properties of the semivariance of uncertain variables are verified. Based on the concept of semivariance of uncertain variables, two types of mean-semivariance diversified models for uncertain portfolio selection are proposed. Since the models are complex, a hybrid intelligent algorithm which is based on 99-method and genetic algorithm is designed to solve the models. In this hybrid intelligent algorithm, 99-method is applied to compute the expected value and semivariance of uncertain variables, and genetic algorithm is employed to seek the best allocation plan for portfolio selection. At last, several numerical examples are presented to illustrate the modelling idea and the effectiveness of the algorithm.