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.
SOA Exam ASTAM
Official syllabus, notation, formula sheet, introductory note, study notes, and released exams are mapped for topic planning.
What the official PDFs establish
- Format
- 3-hour exam with six questions and 60 total points.
- Excel component
- One question is answered in an Excel workbook; five questions are answered in written booklets.
- Assumed knowledge
- FM, P, FAM, and mathematical statistics VEE are assumed.
- Submission split
- The Excel workbook is uploaded for the Excel question, while answer booklets are submitted for the written questions.
- Tables and formula access
- Paper tables and the paper formula sheet are not supplied; candidates use the provided Excel workbook and official electronic resources.
Topic and domain coverage
| Topic | Weight | Source |
|---|---|---|
| Severity Models | 8-18% | Source: Exam ASTAM Syllabus, p. 2 |
| Aggregate Models | 12-22% | Source: Exam ASTAM Syllabus, p. 2 |
| Coverage Modifications | 8-18% | Source: Exam ASTAM Syllabus, p. 2 |
| Construction and Selection of Parametric Models | 14-24% | Source: Exam ASTAM Syllabus, p. 3 |
| Credibility | 12-20% | Source: Exam ASTAM Syllabus, p. 3 |
| Reserving and Pricing | 15-29% | Source: Exam ASTAM Syllabus, p. 4 |
Chapter and reading intelligence
- Loss Models, fifth edition
Selected sections from chapters 3, 5, 7-9, 11-13, 15, 17, and 18 are mapped in the syllabus.
- Introduction to Ratemaking and Loss Reserving
Selected sections from chapters 1, 4, and 5 are listed for ratemaking and loss reserving context.
- Outstanding Claims Reserves and QERM Chapter 5
Study notes support reserving and risk-measure topics; the guide summarizes concepts and links official materials.
Official files used by the map
- Official syllabussyllabus
Primary source for format, topic weights, and readings.
Source: Spring 2026 Exam ASTAM Syllabus - Notation guidenotation
Use for notation consistency in examples.
Source: ASTAM Notation for Spring 2026 - Formula sheetformula-sheet
Use to separate supplied formulas from skills that still need memory and practice.
- Introductory study notestudy-note
Use for exam logistics, Excel workbook submission, and software expectations.
- Released ASTAM exams and solutionsreleased-exam
Use for topic maps and answer-style analysis; do not republish questions or solutions.
Source: April 2026 ASTAM Exam
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 exam 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.