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Extremal quantities and value-at-risk

Victor Chernozhukov

This article looks at the theory and empirics of extremal quantiles in economics, in particular value-at-risk. The theory of extremes has gone through remarkable developments and produced valuable empirical findings in the last 20 years. In the discussion, we put a particular focus on conditional extremal quantile models and methods, which have applications in many areas of economic analysis. Examples of applications include the analysis of factors of high risk in finance and risk management, the analysis of socio-economic factors that contribute to extremely low infant birthweights, efficiency analysis in industrial organization, the analysis of reservation rules in economic decisions, and inference in structural auction models. Keywords: Extremes, Quantiles, Regression, Value-at-risk, Extremal Bootstrap. JEL Classifications: C13, C14, C21, C41, C51, C53.

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