The definition of risk is based on two main concepts: the possibility of 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 set is a sub-class of coherent, convex or co-monotone risk measures, conform the properties of the two components  .
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 .
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. 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