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