Before revision:  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  .
After revision:  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 . 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 .