  The intuition of risk is based on two main concepts: loss and variability. In
this paper, we present a composition of risk and deviation measures, which
contemplate these two concepts. Based on the proposed Limitedness axiom, we
prove that this resulting composition, based on properties of the two
components, is a coherent risk measure. Similar results for the cases of convex
and co-monotone risk measures are exposed. We also provide examples of known
and new risk measures constructed under this framework in order to highlight
the importance of our approach, especially the role of the Limitedness axiom.
