中文摘要：

本文针对随机占优研究中，资产组合有效性检验中仅考虑风险资产的现状，将其延伸到包含无风险资产层面，提出扩展一阶占优准则，并给出解决此类问题的线性规划方法。通过对线性规划结果的分析，结合投资者选定的基准市场组合，本文给出资产组合有效性的划分依据，明确了投资者的选择目标。文章最后通过一个简单算例说明了引入无风险资产后的合理性和可操作性，及其对投资者决策结果的影响。

英文摘要：

Most of the efforts of the portfolio efficient analysis only concerned the risk assets, that is to say, regardless of the riskless asset. In order to provide robust results, this paper relaxes the first stochastic dominance criteria, and takes the riskless asset into consideration. The introduction of riskless asset requires an overview method to focus on operational tests of portfolio efficiency. As a result, the emphasis of the paper is to construct a linear programming model which is based on the first degree stochastic dominance with a riskless asset. The corresponding results from the model, together with the quantitative analysis related to benchmark set established beforehand, could therefore verify whether the objective asset is efficient. From the approach mentioned above, it is clear that decision makers will select portfolios aiming at a high profit since they weren＇t dominated by benchmark set. At last, a simple numerical answer is presented to reflect the application when making selective decision.