A decomposition of a sub-class of spectral risk measures is introduced in terms of L-moments accounting for geometric characteristics of the return distribution similar to the ones described by the ordinary moments. The decomposition characterizes completely the spectral risk measures with...

The paper introduces a new, moment-based representation of version independent, coherent risk functionals for distributions with a finite second moment. The representation is based on L-moments. We analyze the second- and the third-order approximations and provide a method for constructing...

In this paper, we provide a stable limit theorem for the asymptotic distribution of the sample average value-at-risk when the distribution of the underlying random variable X describing portfolio returns is heavy-tailed. We illustrate the convergence rate in the limit theorem assuming that X has...

Portfolio risk estimation in volatile markets requires employing fat-tailed models for financial returns combined with copula functions to capture asymmetries in dependence and an appropriate downside risk measure. In this survey, we discuss how these three essential components can be combined...

In the post-crisis era, financial institutions seem to be more aware of the risks posed by extreme events. Even though there are attempts to adapt methodologies drawing from the vast academic literature on the topic, there is also skepticism that fat-tailed models are needed. In this paper, we...