Abstract
The purpose of this paper is to show that the use of heavy-tailed distributions in Financial problems is theoretically baseless and can lead to significant misunderstandings. The reason for this the authors see in an incorrect interpretation of the concept of the distributional tail. In accordance with this, in applications it is necessary to use instead of the distributional tail the "smearing" of its central part. keywords: heavy tailed distributions, exponential tails, pre-limit theorems, Financial indexes
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