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The supremacy of the stable Paretian distributions over the Gaussian distribution is by now a stylized fact in the financial theory and practice. It is well known that the asymptotic inference about the expected returns is not always reliable and that the nonparametric bootstrap can be used as an alternative. However, several studies have emphasized the fact that the nonparametric bootstrap is invalid for the stable Paretian distributions. The reason is that the expected returns are highly influenced by the risk of the investment opportunities, risk which is always greater in a stable Paretian financial market than in a Gaussian market. In this monograph a refined bootstrap method that overcomes the drawbacks of the nonparametric bootstrap is introduced.