Skin in the Game

by Nassim Nicholas Taleb

  Our interest is in distinguishing between cases where tail events dominate impacts, as a formal definition of the boundary between the categories of distributions to be considered as Mediocristan and Extremistan. The natural boundary between these occurs at the subexponential class, which has the following property:

  Let X = be a sequence of independent and identically distributed random variables with support in (ℝ+), with cumulative distribution function F. The subexponential class of distributions is defined by (see Teugels 1975, Pitman 1980):

  where