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Integrating Systemic Risk and Risk Analysis Using Copulas

International Journal of Disaster Risk Science 2018年第4期9卷 561-567页

作者： stefan Hochrainer-Stigler Georg Pflug Ulf Dieckmann Elena Rovenskaya stefan thurner Sebastian Poledna Gergely Boza Joanne Linnerooth-Bayer Ake Brannstrom International Institute for Applied Systems Analysis(IIASA) 2361 LaxenburgAustria Department of Statistics and Operations Research University of Vienna1010 ViennaAustria Complexity Science Hub 1080 ViennaAustria Faculty of Computational Mathematics and Cybernetics Lomonosov Moscow State UniversityMoscowRussia 119234 Medical University of Vienna 1090 ViennaAustria Santa Fe Institute Santa FeNM 87501USA Evolutionary Systems Research Group MTA-oK-BLI Centre for Ecological ResearchHungarian Academy of SciencesTihany 8237Hungary Department of Mathematics and Mathematical Statistics Umea University90187 UmeaSweden

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 copulasdescribing 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.

关键词： Copulas Individual risk Risk analysis Systemic risk

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