efficient frontier造句

Following , making development study from the three directions : the first one is how to reduce calculation when to use markowitz model . this text has improved the efficient frontier of markowitz model utilizing free risk assets , and reduced calculation about revenue rates " co - variance matrix utilizing single or multiple factors , and so on . the second one is to add thinking factors about , such as transaction fee , fund limitation , lowest transaction unit ' s limitation , risk measures and exchange rate risk of international portfolio securities , so as to make markowitz model closer to our country ' s practice
接着，分三今方向对markowitz模型进行了拓展研究：第一个方向是运用markowitz模型时如何减少计算量，本文利用无风险资产来改进markowitz模型的有效边界，利用单因子或多因子模型来减少收益率协方差的计算量等等；第二个方向是增加考虑因素，诸如交易费用、资金限制、最小交易单位限制，风险测度和国际组合证券的汇率风险，使markowitz模型更贴近我国的实际；第三个方向是对markowitz模型进行动态拓展研究，提出了将证券收益率看成是随机序列时的投资决策模型，深入研究了m ? v有效边界随资产品种数增加而发生的漂移，并用解析方法和几何图形描述了漂移的轨迹和方向。
It's difficult to find efficient frontier in a sentence. 用efficient frontier造句挺难的

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