Leshno和Levy(2002)透過將隨機優勢延伸擴展為幾乎隨機優勢(Almost Stochastic Dominance,ASD)，藉此排除一些「病態」效用函數(Pathological Function)，之所以稱為「病態」效用函數是因為數學上成立但實務上投資者做決策時並不會以此作為其決策偏好。
然而，Leshno和Levy(2002)所提出的幾乎隨機優勢雖然被廣泛運用於找出有效之投資組合，但Tzeng et al. (2013)發現他們所定義之幾乎二階隨機優勢(Almost Second-Order Stochastic Dominance,ASSD)並無法滿足原先隨機優勢理論中之期望效用最大化性質，因此重新修正幾乎二階隨機優勢以滿足此性質。
Tzeng et al. (2013)重新定義幾乎二階隨機優勢後，雖然解決無法滿足期望效用最大化的問題，但在此修正下亦產生了新的問題－無法滿足隨機優勢理論中另一個主要性質－階層性質(Hierarchy Theory)，此項性質如同期望效用最大化的性質，對於經濟與財務上投資效率集合的分析上來說相當地重要。
因此，此篇論文嘗試著重新修正原先Leshno和Levy(2002)所提出之幾乎二階隨機優勢與效用函數，使得修正後的幾乎隨機優勢理論保有原本隨機優勢理論的重要性質，能夠同時滿足期望效用最大化的性質與階層性質，藉此更有效率的找出有效之投資組合，並提出演算法則使得能夠實際執行於實例分析中。

Leshno and Levy (2002) established almost stochastic dominance (ASD) to reveal a preference for most decision makers , but not for all of them.Although almost stochastic dominance is widely used to find the efficient investment sets,Tzeng et al. (2013) found that almost stochastic dominance established by Leshno and Levy (2002) does not have expected-utility maximization.Therefore, Tzeng et al. (2013) revised almost stochastic dominance.Almost stochastic dominance defined by Tzeng et al. (2013) has hierarchy property but not the expected-utility maximization.
Therefore,we give a new definition for almost stochastic dominance and revised the utility function.The new almost stochastic dominance has both hierarchy property and the expected-utility maximization.We further provided the algorithm which let almost stochastic dominance can be executed in data analysis.

第一章 緒論-------------------------1
第二章 幾乎隨機優勢模型探討-----------3
第三章 修正後幾乎隨機優勢理論---------10
第四章 幾乎二階隨機優勢理論演算法則----16
第五章 模擬分析----------------------19
第六章 實例分析----------------------22
第七章 結論-------------------------30
附錄-------------------------------31
參考文獻----------------------------41

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