Whether entropy is more suitable to measure risk of portfolio or the portfolio diversification, actually, is an endless controversy. So, as the risk measurement and the portfolio diversification measure, entropy is respectively introduced to MV model, obtaining entropy based portfolio models. Meanwhile, higher moments (skewness and kurtosis) are recommended to relax the assumption of normal distribution and reflect the extreme events. Furthermore, consideration of robust optimization approach estimates the uncertain input parameters in these models; subsequently, entropy based robust portfolio models with higher moments are constructed. Moreover, multiobjective particle swarm optimization is applied to tackle these sophisticated portfolio models. Eventually, empirical comparisons indicate that entropy is more suitable to diversify the portfolio; importantly, robust portfolio models taking entropy as the measure of the portfolio diversification can provide the optimal portfolios, and significantly improve portfolio performances. Additionally, higher moments should not be ignored in the entropy based portfolio models.

熵更适合衡量投资组合的风险还是投资组合的多元化，实际上是一个无休止的争论。因此，作为风险度量和投资组合多样化的度量，熵分别被引入到 MV 模型中，得到基于熵的投资组合模型。同时，建议使用较高的矩（偏度和峰度）来放松正态分布的假设并反映极端事件。此外，考虑稳健优化方法估计这些模型中的不确定输入参数；随后，构建具有更高矩的基于熵的稳健投资组合模型。此外，应用多目标粒子群优化来处理这些复杂的投资组合模型。最终，实证比较表明熵更适合分散投资组合；重要的是，以熵作为投资组合多元化度量的稳健投资组合模型可以提供最优投资组合，并显着提高投资组合绩效。此外，在基于熵的投资组合模型中不应忽略更高的矩。