Some Contra-Arguments for the Use of Stable Distributions in Financial   Modeling
  In the present paper, we discuss contra-arguments concerning the use of Pareto-Lev\'y distributions for modeling in Finance. It appears that such probability laws do not provide sufficient number of outliers observed in real data. Connection with the classical limit theorem for heavy-tailed distributions with such type of models is also questionable. The idea of alternative modeling is given. 
Lev B. Klebanov, Greg Temnov, Ashot V. Kakosyan
stat.AP q-fin.MF