Abstract
Systemic risk describes the phenomenon that dependency adds a specific component of risk to a system or network of (financial) institutions as a whole, which would not be present if the institutions were independent from each other. This paper introduces the concept of systemic risk measures. We describe and study its behavior as a function of the copula, which represents the loss variables of the institutions in the network. Further, we define stochastic order relations on copulas and relate them with systemic risk measures.
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Notes
The relation to stochastic second order dominance (\(X\prec _{ssd}Y\) iff \({{\mathrm{{\mathbb {E}}}}}g(X)\le {{\mathrm{{\mathbb {E}}}}}g(Y)\) for all monotonic concave functions) is given by: \(X\prec _{sl}Y\) iff \(Y\prec _{ssd}X\).
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We would like to thank the guest editor and the two anonymous referees for insightful comments which help us significantly strengthen this paper.
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This paper is dedicated to Walter Gutjahr.
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Pflug, G.C., Pichler, A. Systemic risk and copula models. Cent Eur J Oper Res 26, 465–483 (2018). https://doi.org/10.1007/s10100-018-0525-z
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DOI: https://doi.org/10.1007/s10100-018-0525-z