Before revision:  As a remedy, we establish the joint identifiability of CoVaR, MES and (CoVaR, CoES) together with the value-at-risk (VaR) of the reference position X . While this resembles the situation of the classical risk measures expected shortfall (ES) and VaR concerning identifiability, a joint elicitability result fails. Therefore, we introduce a completely novel notion of multivariate scoring functions equipped with some order, which are therefore called multi-objective scores.
After revision:  As a remedy, we establish the joint identifiability of CoVaR, MES and (CoVaR, CoES) together with the value-at-risk (VaR) of the reference position X , but show that an analogue result for elicitability fails. The novel notion of multivariate scoring functions equipped with some order, which are therefore called multi-objective scores.