ASTAM Severity Models
ASTAM severity models cover claim-size distributions and their tails: parameter effects, transformed distributions, hazard and mean-excess behavior, and the GEV/GPD tools used for extreme losses.
Quick Answer
The Spring 2026 ASTAM syllabus gives severity models an 8-18% weight. The explicit outcomes include parameter effects, transformations, tail comparisons, moments, hazard rates, mean excess functions, and GEV/GPD tail-risk calculations.
This is the first ASTAM block because every later short-term model needs a claim-size distribution. Aggregate losses, reinsurance, reserves, and capital all inherit the severity tail.
What To Know Cold
Know the standard severity families: gamma, lognormal, Pareto, Weibull, transformed beta, and extreme-value forms. For each, be able to say what the parameters do to scale, skewness, and tail weight.
Tail comparisons are more important than isolated density formulas. ASTAM can ask whether one model has heavier limiting tail behavior, a higher hazard at large x, a larger mean excess function, or a better fit to high-layer losses.
GEV And GPD Role
GEV enters through block maxima: annual maximum losses, maximum event sizes, or maximum claim amounts over repeated periods. GPD enters through threshold exceedances: losses above an attachment point, high deductibles, or catastrophe layers.
The actuarial question is not just fitting a distribution. It is estimating a tail probability, Value-at-Risk, Expected Shortfall, or layer premium where ordinary body-fit diagnostics are weak.
Original Practice Drill
Given two fitted severity models with the same mean but different tail behavior, calculate one 95th percentile, one limited expected value, and one mean excess value at a high threshold. Then state which model is more conservative for excess-of-loss pricing.
A complete answer includes the numeric comparison and the explanation. The explanation should identify whether the decision is driven by body fit, high-threshold behavior, or parameter uncertainty.
Common Traps
Trap 1: treating a better body fit as proof of a better tail fit. A model can fit the middle well and still understate high-layer severity.
Trap 2: mixing up survival, density, hazard, and mean excess. They answer different questions: probability beyond x, mass near x, instantaneous failure rate, and average excess above x.
Trap 3: using GPD with too few exceedances and then reporting the estimate as if it were stable. Threshold choice is a modeling judgment.
Original Source-Backed Practice
3 questions built from syllabus outcomes and released-exam patterns. The prompts and answers are original, so they train the skill without copying official exam text.
ASTAM Severity Tail Drill
Tail-focused practice for quantiles, limited expectations, mean excess, and GPD threshold thinking.
- Question 1/Written Answer
Same mean, different tail
Two fitted severity models have the same mean, but Model B has a larger high-threshold mean excess function. Which model is usually more conservative for excess-of-loss pricing, and why?
Solution And Grading Points
Model B is usually more conservative for excess-of-loss pricing because it places more expected severity above high attachment points. The decision is tail-driven, not mean-driven.
- Chooses the model with larger high-threshold mean excess.
- Connects the choice to excess-of-loss pricing.
- States that equal means do not imply equal layer costs.
- Question 2/Written Answer
GPD threshold caveat
What modeling judgment should be stated when using a GPD for losses above a high threshold?
Solution And Grading Points
State why the threshold is high enough for tail modeling but still leaves enough exceedances for estimation. Then report tail estimates as threshold-sensitive.
- Mentions threshold height.
- Mentions number of exceedances.
- Flags sensitivity instead of presenting the estimate as final truth.
- Question 3/Flashcard
Hazard versus survival
What is the conceptual difference between survival S(x) and hazard h(x) for a claim severity model?
Solution And Grading Points
S(x) is the probability the loss exceeds x. The hazard h(x) is the local failure or exceedance rate at x conditional on having reached x.
- Defines survival as a tail probability.
- Defines hazard conditionally.
- Avoids using density, survival, and hazard as interchangeable quantities.