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We establish dual representations for systemic risk measures based onacceptance sets in a general setting. We deal with systemic risk measures ofboth "first allocate, then aggregate" and "first aggregate, then allocate"type. In both cases, we provide a detailed analysis of the correspondingsystemic acceptance sets and their support functions. The same approachdelivers a simple and self-contained proof of the dual representation ofutility-based risk measures for univariate positions.

Dual representations for systemic risk measures based on acceptance sets