This paper is concerned with linear portfolio value-at-risk (VaR) and expected shortfall (ES) computation when the portfolio risk factors are leptokurtic, imprecise and/or vague. Following Yoshida (2009), the risk factors are modeled as fuzzy random variables in order to handle both their random...

We propose a generalization of the decomposition by population subgroups of the α-Gini index, the so-called multi-level subgroup decomposition. We demonstrate that all components obtained from the decomposition, can integrate in their functional form a parameter of inequality sensitivity being...