Extreme Value Theory and Its Applications in Quantitative Risk Management

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Description

This short course pertains to an introduction of Extreme Value Theory (EVT), a branch of probability concerned with the limiting laws of extreme values in large samples, which has found fruitful applications in the study of Quantitative Risk Management (QRM) converging various fields such as Actuarial Science, Engineering, Environmetrics, Math Finance, etc.

This short course contains two major thrusts.  In the first thrust, students will learn the theoretical foundation of EVT.  In particular, we will focus on two types of statistical models by EVT, namely certain maxima models with grouping, and the threshold exceedances models via theory of point processes. The multivariate treatment in light of the dependence structure among variables, will also be discussed.  

The second thrust of the course aims to shed light on the practical usefulness of EVT via its connections to the study of QRM.  We will begin by defining a number of fundamental concepts and quantitative approaches for (financial) risk measurement.  Then we will apply EVT to furnish a set of useful computation tools for evaluating risk measures that are defined based on tail risk scenarios.   Finally, we will review the use of multivariate EVT for constructing flexible models to study dependent risks.