The paper discusses application of stochastic programming approach to the portfolio selection problem involving estimation risk. It focuses on problems aiming at assuring that the portfolio risk does not exceed a given limit with high probability. For solving the problems the sample approximation approach is proposed for which the most important issues like a method used for generating subsamples, setting the correct number of subsamples and empirical confidence level parameter are discussed. As far as the first issue is concerned a bootstrap approach was superior to Monte Carlo method in a simulation study based on returns data of stocks listed on the Warsaw Stock Exchange. For the latter problems it is advised changing the empirical confidence level parameter instead of the number of subsamples to match expected confidence level of the stochastic program. It is also shown that the discussed approach is suitable for investors with high risk aversion.121-136
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