Stefan Hochrainer-Stigler, Georg Pflug, Ulf Dieckmann, Elena Rovenskaya, Stefan Thurner, Sebastian Polend, Gergely Boza, Joanne Linnerooth-Bayer and Ake Braennstroem

Systemic risk research is gaining traction across diverse disciplinary research communities, but has as yet not been strongly linked to traditional, well-established risk analysis research. This is due in part to the fact that systemic risk research focuses on the connection of elements within a system, while risk analysis research focuses more on individual risk to single elements. We therefore investigate how current systemic risk research can be related to traditional risk analysis approaches from a conceptual as well as an empirical point of view. Based on Sklar's Theorem, which provides a one-to-one relationship between multivariate distributions and copulas, we suggest a reframing of the concept of copulas based on a network perspective. This provides a promising way forward for integrating individual risk (in the form of probability distributions) and systemic risk (in the form of copulas describing the dependencies among such distributions) across research domains. Copulas can link continuous node states, characterizing individual risks, with a gradual dependency of the coupling strength between nodes on their states, characterizing systemic risk. When copulas are used for describing such refined coupling between nodes, they can provide a more accurate quantification of a system's network structure. This enables more realistic systemic risk assessments, and is especially useful when extreme events (that occur at low probabilities, but have high impacts) affect a system's nodes. In this way, copulas can be informative in measuring and quantifying changes in systemic risk and therefore be helpful in its management. We discuss the advantages and limitations of copulas for integrative risk analyses from the perspectives of modeling, measurement, and management.