Today I realized a quite known fact. The
log transformation of a random variable, drawn from a fat tail distribution, maps into an exponential tail distribution. My question is very simple:
Is the logarithm sufficient to tame every distribution?
I don't know distributions that are more extreme of the Pareto distribution, then I think so, but I don't know how to prove it. This doubt came from the observation, that peoples in finance tame their random variables with logarithms, but seems they have very bad times during financials earthquakes.