To cope with the short selling issue, this research proposes four models based on the Mean- variance model (MV-model) which frees one from the limitation of short selling. In the first two models, the number and then the proportion of short selling in the portfolio selection are minimized, respectively. In the third model, return, risk, the number of sold short, and the number of total selected securities are viewed as four criteria to be optimized, which can be considered simultaneously by multiple objective programming. In order to eliminate the trade-off between return and risk, the concept of De Novo programming is applied in the fourth portfolio selection model, which can show the least budget, needed to achieve these two conflicting goals at the same time. An empirical data set is tested to verify these four models. KeywordsMean-variance model, short selling, De Novo programming, multiple criteria decision making
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