Higher Moments Portfolio Optimization Considering Entropy based on Polynomial Idealistic Programming

chooseing the optimal portfolio is an integral issue in investment. It is challenging to estimate the tock return rate because of the vague nature of future events. Hence, it is recommended to add diverdity to cover the related risks. According to Markowitz’s modern portfolio theory, assets return has normal distribution. But empirical evidences show that assets return distribution is not normal and we would consider higher moment and Entropy as diversification indexes in this paper. In this study, a new approach for polynomial idealistic programming which is basedon a mean-variance-skewness-kurtosis-entropy model is proposed and two measures of Shannon entropy and Gini-Simpson entropy are used. The results indicated that the proposed approach is well-suited, especially for portfolio models with higher moments. The findings showed that using entropy as a diversification index cannot cause any significant decrease in optimized values for other goals. Using Shannon entropy and Gini-Simpson entropy models can lead to an increase in return and Shannon entropy model can yield more diversification compared to Gini-Simpson entropy model.