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

A reinsurer uses annual block maxima of fire losses. Which is a recognised drawback of the block maxima method compared with peaks over threshold?

The block maxima method keeps only the single largest loss per block, so other large losses in the same block are discarded. This wastes tail information, which is why peaks over threshold is often preferred when data are limited.

  1. AIt cannot be applied to independent data
  2. BIt requires the losses to be normally distributed
  3. CIt may discard useful data, since only one value per block is used and other large losses in the same block are ignoredCorrect
  4. DIt always gives a negative shape parameter
  5. It uses all observations above a high threshold

Explanation

Block maxima keeps only the largest observation in each block, so a second large loss in the same year is ignored. This wastes information about the tail. Peaks over threshold uses all exceedances.

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