 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. Under this perspective, we propose a specific formulation that generates, from any coherent measure, a generalized deviation based on the dispersion of results worse than it, which leads to a very interesting risk measure. Moreover, we present some examples of risk measures that lie in our proposed class .
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 .
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The definition of risk is based on two main concepts: the possibility of loss, and variability.
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class of risk measures composed of coherent risk measures with generalized deviation measures
composition of risk and deviation measures, which capt these two concepts
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proposed
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risk measures. We present extensions of this result for the case of
,
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coherent risk measures. Under this perspective, we propose a specific formulation that generates, from any coherent measure, a generalized deviation based on the dispersion of results worse than it, which leads to a very interesting risk measure. Moreover, we present some examples of risk measures that lie in our proposed class
risk measures, conform the properties of the two components