A novel fuzzy dominant goal programming for portfolio selection with systematic risk and non-systematic risk

In this paper, we consider a fuzzy portfolio selection problem with systematic risk and non-systematic risk simultaneously. These two kinds of risks are measured by beta coefficient and random error variance obtained by Sharp Single Index Model. The total risk as the objective of portfolio decision is obtained by weighting the two kinds of risk. Among them, the weight of systematic risk [Formula: see text] is regarded as the degree of investors' attention to system risk in economic sense. In addition, the fuzzy return and the degree of diversification are measured by triangular fuzzy number and entropy, respectively. And they are also considered the goal of investment decisions. Hence, a tri-objective portfolio is proposed in this paper. For the fuzzy objectives in the model, a goal programming method based on fuzzy dominance is proposed, which can help investors better capture the ideal point of fuzzy returns according to their risk preference. Finally, combined with the systematic impact of COVID-19 on the financial market, we make an empirical analysis based on our proposed model. The results show that the total risk will be on the high side when [Formula: see text] value is too large or too small. That means paying too much or little attention to the systematic risk will lead investors to bear more risk. In addition, when investors ignore the systematic risk; that is, the [Formula: see text] value is low, and investors will concentrate their funds in the same industry.