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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to extreme value theory

In the Peaks over Threshold (POT) approach to extreme value theory, which statement best describes the quantity that is modelled with the Generalised Pareto Distribution (GPD)?

The GPD is used for the excesses over a high threshold, conditional on the observation exceeding that threshold. Block maxima over fixed periods are instead modelled by the generalised extreme value distribution, which is a different approach from peaks over threshold.

  1. AThe block maxima of losses taken over fixed periods
  2. BThe excesses of observations over a high threshold, conditional on the threshold being exceededCorrect
  3. CAll observations below the threshold, after standardisation
  4. DThe number of exceedances per year, which is assumed to be GPD
  5. The sample mean of all losses in the dataset

Explanation

POT considers only observations exceeding a high threshold u and models the excesses X-u given X>u with a GPD. Block maxima are modelled by the GEV distribution instead, so the first option describes a different method.

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