近年來的研究顯示，不同資產之收益分佈於尾端收斂的速度並不一致，多尾橢圓分佈可透過尾端函數來描述此現象。本論文中，我們探討服從多尾橢圓分佈的資產的最佳投資組合問題。我們亦建議一種能連結傳統橢圓分佈並於實際意義上有較好的解釋的特殊形式的之主成分尾端函數，並且提供估計此尾端函數的方法。最後以道瓊工業指數所含之28種資產數據為例，提出最佳投資組合。

Recent studies show that the decreasing rate of tail varies from different asset returns. Multi tail elliptical distribution can describe this phenomenon through tail function. In this thesis, we discuss the optimal portfolio problem for the multi tail elliptical distributed assets. We also present a new type of principal component tail function which connects to the elliptical distribution with better interpretation. A procedure for estimating such tail function is provided. As an empirical study, the optimal portfolio is obtained from the data containing the daily log return of 28 assets from the Dow Jones Industrial Average.

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