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      Dual representations for systemic risk measures

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      Author(s)
      Ararat, Çağın
      Rudloff, B.
      Date
      2020
      Source Title
      Mathematics and Financial Economics
      Print ISSN
      1862-9679
      Publisher
      Springer
      Volume
      14
      Issue
      1
      Pages
      139 - 174
      Language
      English
      Type
      Article
      Item Usage Stats
      122
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      Abstract
      The financial crisis showed the importance of measuring, allocating and regulating systemic risk. Recently, the systemic risk measures that can be decomposed into an aggregation function and a scalar measure of risk, received a lot of attention. In this framework, capital allocations are added after aggregation and can represent bailout costs. More recently, a framework has been introduced, where institutions are supplied with capital allocations before aggregation. This yields an interpretation that is particularly useful for regulatory purposes. In each framework, the set of all feasible capital allocations leads to a multivariate risk measure. In this paper, we present dual representations for scalar systemic risk measures as well as for the corresponding multivariate risk measures concerning capital allocations. Our results cover both frameworks: aggregating after allocating and allocating after aggregation. As examples, we consider the aggregation mechanisms of the Eisenberg–Noe model as well as those of the resource allocation and network flow models.
      Keywords
      Systemic risk
      Risk measure
      Financial network
      Dual representation
      Convex duality
      Penalty function
      Relative entropy
      Multivariate risk
      Shortfall risk
      Permalink
      http://hdl.handle.net/11693/53450
      Published Version (Please cite this version)
      https://dx.doi.org/10.1007/s11579-019-00249-7
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      • Department of Industrial Engineering 733
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