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

A GPD with shape ξ and scale β is fitted to excesses over a threshold. For which value of ξ do the excesses have an infinite mean?

The mean of a GPD is β/(1-ξ), which exists only when ξ is less than 1. At ξ equal to 1 the mean becomes infinite, whereas the other listed values give finite means.

  1. Aξ = 0
  2. Bξ = 0.5
  3. Cξ = 0.9
  4. Dξ = 1Correct
  5. ξ = -0.5

Explanation

The GPD mean is β/(1-ξ), which exists only for ξ<1. At ξ=1 the mean is infinite, and for ξ>1 also. Values 0, 0.5 and 0.9 give finite means, and ξ=-0.5 gives a bounded support.

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