Third Degree Stochastic Dominance and Mean-Risk Analysis
将Ogryczak和Ruszczyński关于二阶随机占优的结果推广到三阶，证明均值下半偏度模型的有效前沿组合在三阶随机占优意义下有效，而均值方差偏度模型组合半有效。
In their recent article, Ogryczak and Ruszczyński (1999) proved that those portfolios associated with the efficient frontiers generated by mean-lower semi-standard deviation model and mean- (lower semi-)absolute deviation model are efficient in the sense of second degree stochastic dominance. This rather surprising result reveals the importance of lower partial risk models in portfolio analysis. In this paper, we extend the results of Ogryczak and Ruszczyński for second degree stochastic dominance to third degree stochastic dominance. We show that portfolios on a significant portion of the efficient frontier generated by mean-lower semi-skewness model are efficient in the sense of third degree stochastic dominance. Also, we prove that the portfolios generated by mean-variance-skewness model are semi-efficient in the sense of third degree stochastic dominance.