Under Solvency II the computation of capital requirements is based on value at risk (V@R). V@R is a quantile-based risk measure and neglects extreme risks in the tail. V@R belongs to the family of distortion risk measures. A serious deficiency of V@R is that firms can hide their total downside risk in corporate groups. They can largely reduce their total capital requirements via appropriate transfer agreements within a group structure consisting of sufficiently many entities and thereby circumvent capital regulation. We prove several versions of such a result for general distortion risk measures of V@R-type, explicitly construct suitable allocations of the group portfolio, and finally demonstrate how these findings can be extended beyond distortion risk measures  .
Under Solvency II the computation of capital requirements is based on value at risk (V@R). V@R is a quantile-based risk measure and neglects extreme risks in the tail. V@R belongs to the family of distortion risk measures. A serious deficiency of V@R is that firms can hide their total downside risk in corporate networks, unless a consolidated solvency balance sheet is required for each economic scenario. In this case, they can largely reduce their total capital requirements via appropriate transfer agreements within a network structure consisting of sufficiently many entities and thereby circumvent capital regulation. We prove several versions of such a result for general distortion risk measures of V@R-type, explicitly construct suitable allocations of the network portfolio, and finally demonstrate how these findings can be extended beyond distortion risk measures . We also discuss why consolidation requirements cannot completely eliminate this problem. Capital regulation should thus be based on coherent or convex risk measures like average value at risk or expectiles .
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groups. They
networks, unless a consolidated solvency balance sheet is required for each economic scenario. In this case, they
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group
network
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group
network
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. We also discuss why consolidation requirements cannot completely eliminate this problem. Capital regulation should thus be based on coherent or convex risk measures like average value at risk or expectiles