Example of Coherent Risk measure with Compact Representation

Every coherent risk measure $$\rho$$ can be represented as $$\rho(X)\triangleq \sup_{Q \in \mathcal{Q}} \mathbb{E}\left[ -X \right],$$ for a set of probability measures $$\mathcal{Q}$$ defined on the same measurable space. Many of which, we know closed-form expression for (ie.: no sup, inf, or limits).

My question is, is there a known coherent risk-measure such that

• $$\rho$$ is coherent
• $$\mathcal{Q}$$ is compact in the set of probability measures, all dominated by a single probability measure $$\mathbb{P}$$.
• (Optional) $$\rho$$ has a known closed-form?