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In the present paper, we discuss contra-arguments concerning the use ofPareto-Lev\'y distributions for modeling in Finance. It appears that suchprobability laws do not provide sufficient number of outliers observed in realdata. Connection with the classical limit theorem for heavy-taileddistributions with such type of models is also questionable. The idea ofalternative modeling is given.

Some Contra-Arguments for the Use of Stable Distributions in Financial Modeling