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Hoffmann, Hannes; Meyer-Brandis, Thilo; Svindland, Gregor (2016): Risk-consistent conditional systemic risk measures. In: Stochastic Processes and their Applications, Vol. 126, No. 7: pp. 2014-2037
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We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional aggregation and a univariate conditional risk measure. Our studies extend known results for unconditional risk measures on finite state spaces. We argue in favor of a conditional framework on general probability spaces for assessing systemic risk. Mathematically, the problem reduces to selecting a realization of a random field with suitable properties. Moreover, our approach covers many prominent examples of systemic risk measures from the literature and used in practice. (C) 2016 Elsevier B.V. All rights reserved.