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Statistical Tools in Finance and Insurance

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Stable laws { also called -stable or Levy-stable { are a rich family of probability distributions that allow skewness and heavy tails and have many interesting mathematical properties. They appear in the context of the Generalized Central Limit Theorem which states that the only possible non-trivial limit of normalized sums of independent identically distributed variables is -stable. The Standard Central Limit Theorem states that the limit of normalized sums of independent identically distributed terms with nite variance is Gaussian ( -stable with = 2). It is often argued that nancial asset returns are the cumulative outcome of a vast number of pieces of information and individual decisions arriving almost continuously.

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