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The present study applies a mathematical optimization method to solve the portfolio selection problem. This is formulated as a semi-infinite programming (SIP) problem and is solved by using a version of the stochastic outer approximation method in MATLAB. This method replaces the original problem with a sequence of optimization finite problems. The results are compared with other portfolio selection strategies such as Markowitz. Numerical experiments are performed using five years of data from eight Colombian companies that trade in the stock market. The results show that the SIP portfolio is similar to the minimum variance portfolio and that both are diversified portfolios. The maximum return portfolio is not diversified and should be discarded. Even though the naive portfolio is diversified, its performance and returns are lower than expected, but its risks are less than that of minimum variance and SIP. It is concluded that the proposed method provides satisfactory solutions when compared to the Markowitz method. [ABSTRACT FROM AUTHOR]

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