We establish dual representations for systemic risk measures based on acceptance sets in a general setting. We deal with systemic risk measures of both “first allocate, then aggregate” and “first aggregate, then allocate” type. In both cases, we provide a detailed analysis of the corresponding systemic acceptance sets and their support functions. The same approach delivers a simple and self-contained proof of the dual representation of utility-based risk measures for univariate positions.

中文翻译：

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基于接受集的系统风险度量的双重表示

我们基于一般情况下的接受集为系统风险度量建立双重表示。我们处理“先分配再汇总”和“先汇总再分配”两种类型的系统风险度量。在这两种情况下，我们都会对相应的系统接受集及其支持功能进行详细分析。相同的方法为单变量头寸的基于效用的风险度量的双重表示提供了简单且独立的证明。