Before revision:  In this paper we present a class of risk measures composed of coherent risk measures with generalized deviation measures . Based on the  Limitedness axiom, we prove that this set is a sub-class of coherent risk measures. We present extensions of this result for the case of convex or co-monotone coherent risk measures.
After revision:  In this paper we present a class of risk measures composed of coherent risk measures with generalized deviation measures . Based on the Limitedness axiom, we prove that this set is a sub-class of coherent , convex or co-monotone coherent risk measures.