This paper proposed the optimal portfolio model maximizing returns and minimizing the risk expressed as CvaR under the assumption that the portfolio yield subject to heavy tail. We use fuzzy mathematics method to solve the multi-objectives model, and compare the model results to the case under the normal distribution yield assumption based on the portfolio VAR through empirical research. It is showed that our return is approximate to M-V model but risk is higher than M-V model. So it is illustrated that CVaR predicts the potential risk of the portfolio, which will help investors to cautious investment.
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