We investigate the set of centers of completely and jointly mixable distributions. In addition to several results, we show that, for each n ≥ 2, there exist n standard Cauchy random variables adding up to a constant C if and only if |C| ≤ n*log(n − 1)/π

In the recent Fundamental Review of the Trading Book (FRTB), the Basel Committee on Banking Supervision proposed the shift from the 99% Value-at-Risk (VaR) to the 97.5% Expected Shortfall (ES) for internal models in market risk assessment. Inspired by the above transition, we introduce a new...

In this paper we provide a general mathematical framework for distributional transforms, which allows for many examples that are used extensively in the literature of finance, economics and optimization. We put a special focus on the class of probability distortions, which is a fundamental tool...