What is Admissible Spectrum

Spectral risk measures are defined as the most attractive subclass of coherent quantile-based risk measures, with a remarkable aptitude for concretizing the decision-maker's subjective attitude toward risk. This chapter raises the problem of underrepresentation of the subclass of spectral risk measures by reviewing the standard spectral risk measures proposed in the literature. In parallel, a discussion about the approaches behind the conception of these risk measures is held. Through this discussion, the authors spot a number of problems with each of these proposals that stand against the reliable applicability of these risk measures in practice.