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?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy