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.