Before revision:  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 .
After revision:  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 , is a coherent risk measure. Similar results for the cases of convex and co-monotone risk measures are exposed.