Extreme value theory is concerned with the study of the asymptotic distribution of extreme events, that is to say events which are rare in frequency and huge in magnitude with respect to the majority of observations. Statistical methods derived from it have been employed increasingly in finance, especially for risk measurement. This paper surveys some of those main applications, namely for testing different distributional assumptions for the data, for Value-at-Risk and Expected Shortfall calculations, for asset allocation under safety-first type constraints, and for the study of contagion and dependence across markets under conditions of stress.
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