  We investigate to which extent the relevant features of (static) Systemic
Risk Measures can be extended to a conditional setting. After providing a
general dual representation result, we analyze in greater detail Conditional
Shortfall Systemic Risk Measures. In the particular case of exponential
preferences, we provide explicit formulas that also allow us to show a time
consistency property. Finally, we provide an interpretation of the allocations
associated to Conditional Shortfall Systemic Risk Measures as suitably defined
equilibria. Conceptually, the generalization from static to conditional
Systemic Risk Measures can be achieved in a natural way, even though the proofs
become more technical than in the unconditional framework.
