Apply the Generalized Extreme Value and the Generalized Pareto distributions to the estimation of tail risk measures and probabilities.
Free SOA Exam ASTAM (Advanced Short-Term Actuarial Mathematics) lesson in Severity Models. 25 min read, ~3,735 words.
GEV fits block maxima with parameters: location, scale, shape. Fréchet (heavy), Gumbel (light), reverse-Weibull (bounded). GPD fits exceedances with parameters. Same as the GEV of the parent. VaR tail formula (GPD):. TVaR closed form (GPD, ):. Mean of GPD excess exists only when; variance only when. Block-max CDF:. Pr at...
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- Content
- Example 1
- Example 2
- Example 3
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- Key Takeaways
- Exam Shortcuts
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- 1f
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