Scenario-based risk evaluation

Abstract Risk measures such as expected shortfall (ES) and value-at-risk (VaR) have been prominent in banking regulation financial risk management. Motivated by practical considerations the assessment management of risks, including tractability, scenario relevance robustness, we consider theoretical properties scenario-based evaluation. We establish axiomatic characterisations that are comonotonic-additive or coherent, obtain a novel ES-based representation result. propose several measures, various versions Max-ES Max-VaR, study their properties. The theory is illustrated with data examples.