Before revision: Conditional risk (co-risk) measures and risk contribution measures are increasingly used in quantitative risk analysis to evaluate the systemic risk that the failure (or loss) of a component spreads to other components or even to the entire system. Co-risk measures are conditional versions of measures usually employed to assess isolated risks, while risk contribution measures evaluate how a stress situation for one component incrementally affects another one. In this article , we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution (\DeltaCoD) measures , which contain the well-known conditional Value-at-Risk (CoVaR) , conditional Expected Shortfall (CoES) , and risk contribution measures in terms of the VaR and ES ( and ) as special cases.
After revision: In this paper , we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution (\DeltaCoD) measures , which contain the well-known conditional Value-at-Risk (CoVaR) , conditional Expected Shortfall (CoES) , and risk contribution measures in terms of the VaR and ES ( and ) as special cases.