1. Introduction

The empirical and theoretical study of heavy-tailed distributions within economics and finance is by now a mature area of research, dating back more than 50 years. The first empirical study is usually attributed to Mandelbrot (1963), who noted that the changes of cotton prices seem to be well approximated by heavy-tailed so-called stable distributions. Loosely speaking, this means that rare events tend to happen much more often than they would if risk distributions had standard Gaussian (or other) thin tails. For example, the approximately 20 % drop of the stock market on the so-called Black Monday of October 19, 1987 would occur much less often than once in a billion years under standard assumptions of Gaussian distributions, and has been taken as evidence that stock market returns are heavy-tailed (see, for instance, the striking examples in Chap. 2 in Stock and Watson 2007 that illustrate inappropriateness of Gaussian distributions as models for financial returns based on their behavior during the Black Monday crisis).