Abstract
In Chap. 1, we introduced the overall approach how to integrate extreme and systemic risk analysis. We discussed that a network perspective is very beneficial in that regard. We informally defined a system to be a set of individual elements which are, at least partly, interconnected with each other. We assumed that these individual elements are “at risk” and we will call such kind of risk “individual risk”. In this chapter, we assume that the risk an individual element within a network is exposed to can be represented as a random variable. Consequently, our focal point for individual risk will be a distribution function. As we are especially interested in downside risk (e.g., losses), we will frequently deal with a so-called loss distribution. For extreme risk, the tails of the distribution function are of great importance. However, for accurately estimating the tail, a theory of its own as well as corresponding techniques are needed, namely extreme value theory, which is the central topic of this chapter.
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Hochrainer-Stigler, S. (2020). Individual Risk and Extremes. In: Extreme and Systemic Risk Analysis. Integrated Disaster Risk Management. Springer, Singapore. https://doi.org/10.1007/978-981-15-2689-3_2
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