邊際條件隨機佔優(Marginal Conditional Stochastic Dominance,MCSD)在Shalit and Yitzhaki(1994)被提出，主要是說在給定投資組合情況下，給出了在什麼條件下可以通過略微增加一個資產並同等減少另一個資產的佔比來增加投資者的期望效用，此投資者屬於所有追求效用最大化且對風險厭惡的群體。邊際條件近乎隨機佔優(Almost Marginal Conditional Stochastic Dominance,AMCSD)在Denuit et al.(2014)被提出，作為MCSD的擴展。
以上的概念都只在二階的範圍討論，即都要求投資者是追求效用最大化和風險厭惡的。本文將把MCSD概念擴展到一階的範圍，即投資者僅追求效用越大越好的情況。還要重新定義AMCSD，相應也提出一階的AMCSD。這樣從一階到二階來構造出一個有層次結構的MCSD理論。再將我們的理論應用於Denuit et al.(2014)中的例子並跟其結果做比較，優化投資建議。
最後再將一階和二階的MCSD理論應用到多資產上，研究能否通過改變改變多個資產的佔比來提高投資者期望效用

Marginal Conditional Stochastic Dominance(MCSD) developed by Shalit and Yitzhaki(1994) states the conditions under which all risk-averse individuals, when presented with a given portfolio, prefer to increase the share of one risky asset over that of another. Almost Marginal Conditional Stochastic Dominance(AMCSD) developed by Denuit et al.(2014) extends this concept to state the conditions under which almost(not all) risk-averse individuals prefer to increase the share of one risky asset over that of another in a given portfolio.

In this paper, we extend this concept to state the conditions under which all and almost individuals who have monotone increasing utility functions behave in this way. And we will revisit AMCSD to construct a hierarchy theory of MCSD. Then we extend the analysis to allow for changes in many securities of a portfolio in order to find a dominating allocation efficiently. A financial application is further provided to demonstrate that using MCSD and AMCSD can indeed improve investment efficiency.

目錄
1 研究動機和目的 1
2 文獻回顧 3
2.1 隨機佔優和近乎隨機佔優 3
2.2 兩資產間的MCSD和AMCSD 5
2.3 多資產改變的MCSD和AMCSD 7
3 重新定義邊際條件隨機佔優 8
3.1 原有MCSD和AMCSD定義 8
3.2 邊際條件一階隨機佔優(MC-FSD) 11
3.3 邊際條件近乎一階隨機佔優(MC-AFSD) 12
3.4 邊際條件近乎二階隨機佔優(MC-ASSD) 14
3.5 兩種定義的比較 16
3.5.1 舉例和計算 16
3.5.2 兩種定義計算結果比較 21
4 多資產改變的邊際條件隨機佔優 22
4.1 投資組合的MC-FSD 22
4.2 投資組合的MC-SSD 25
4.3 投資組合的MC-AFSD 28
4.4 投資組合的MC-ASSD 31
5 實例分析 34
5.1 資料介紹 34
5.2 MCSD的應用之一 36
5.2.1 兩兩資產的比較 36
5.2.2 多資產改變 40
5.3 MCSD的應用之二 44
5.3.1 含有BXM的投資組合優化建議 44
5.3.2 含有BXY的投資組合優化建議 46
5.3.3 含有BFLY的投資組合優化建議 48
6 結論 51
參考文獻 52
附錄 54

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