In certain cases partial sums of i.i.d. random variables with finite variance are better approximated by a sequence of stable distributions with indices \alpha_n \to 2 than by a normal distribution. We discuss when this happens and how much the convergence rate can be improved by using...

Estimators of the extreme-value index are based on a set of upper order statistics. We present an adaptive method to choose the number of order statistics involved in an optimal way, balancing variance and bias components. Recently this has been achieved for the similar but somewhat less...

The paper characterizes first and second order tail behavior of convolutions of i.i.d. heavy tailed random variables with support on the real line. The result is applied to the problem of risk diversification in portfolio analysis and to the estimation of the parameter in a MA(1) model.