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Exam ASTAM topic · 20–30% of exam

Loss Reserving

Loss development and reserving methods including chain ladder, Bornhuetter-Ferguson, Cape Cod, and frequency-severity approaches.

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Per-objective worked-example outlines

For each learning objective on Loss Reserving, here is the approach an exam item would test — the setup, the ordering of your reasoning, and the formula or identity you need to bring to the page. Approaches, not full solutions, by design. Verify against the current soa.org syllabus before your sitting.

Project ultimate losses using chain ladder development factors

Setup

A 10x10 loss development triangle is given and you must compute selected age-to-age factors, ultimate losses, and IBNR.

Approach

Compute volume-weighted age-to-age factors as ratios of successive cumulative columns. Select factors (all-years, latest k, or excluding outliers). Apply selected factors and a tail factor to project each accident year's latest diagonal to ultimate. IBNR = projected ultimate - reported. Compute by accident year and total.

Key identity

CDF_i = Π_j ATU_j; ULT_i = reported_i × CDF_i; IBNR = ULT - reported.

Apply Bornhuetter-Ferguson and Cape Cod methods with a priori expectations

Setup

Recent accident years have very immature reporting; you must apply BF and Cape Cod methods using an a priori loss expectation.

Approach

BF: ULT_i = reported_i + (a priori expected ultimate) × (1 - 1/CDF_i). Cape Cod estimates the a priori internally as Σ reported / Σ (used-up exposure), where used-up exposure = on-level premium × (1/CDF_i). Cape Cod is BF with an internally derived a priori; both stabilize the immature years.

Key identity

BF: ULT = reported + a priori × (1 - 1/CDF). Cape Cod estimates a priori from the data.

Evaluate reserve uncertainty using stochastic methods

Setup

A reserving exercise produces a point estimate, but management wants a range and probability of adequacy.

Approach

Use stochastic methods: Mack's formula for chain ladder gives mean squared error of reserves analytically. Bootstrap chain ladder resamples residuals to build a distribution of reserves. GLM-based stochastic reserving (e.g., over-dispersed Poisson) provides a parametric distribution. Report a percentile range (e.g., 75th percentile).

Key identity

Mack: closed-form CL MSE. Bootstrap: empirical distribution from resampled residuals.

Common exam traps on Loss Reserving

Recurring patterns where candidates lose points on Loss Reserving-style items. Each entry pairs the trap with the fix.

Trap

Including a tail factor only in some accident years.

Fix

Apply the tail consistently; if you tail one year, tail them all.

Trap

Confusing reported, paid, and incurred triangles.

Fix

Each has its own development pattern; do not mix triangles in a single development factor calculation.

Trap

Using volume-weighted factors without considering outlier years.

Fix

Investigate large factors before selecting; consider all-year average or simple averages as alternatives.

Trap

Equating Cape Cod with BF without recognizing internal a priori estimation.

Fix

Cape Cod is BF; the difference is how the a priori is derived (internal vs external).

Where to find Loss Reserving in popular manuals

Pointers to where each major vendor covers this topic, so you can grab the right chapter without combing the full manual. We do not reproduce vendor content — just the location. Chapter and lesson numbers shift between editions; use these as a guide, not as a citation.

ASM

Loss reserving chapters in the ASTAM manual

ACTEX

Chain ladder, BF, Cape Cod, and stochastic reserving chapters

Coaching Actuaries

Learn modules on Loss Reserving; Adapt category "Loss Reserving"

7-day Loss Reserving micro plan

A focused 7-day sub-schedule for Loss Reserving specifically, at roughly 1.5–2.5 hours per day. Drop it inside your full Exam ASTAM plan as a single coverage module.

Day 1

Read the chain ladder chapter; build flashcards on age-to-age factors and tail factor selection.

Day 2

Drill 6 chain ladder problems on 5x5 to 10x10 triangles.

Day 3

BF method — 6 problems applying a priori expectations to immature years.

Day 4

Cape Cod method — 5 problems including the internal a priori derivation.

Day 5

Stochastic reserving — 4 problems on Mack and 2 on bootstrap.

Day 6

Written-answer practice — 3 multi-step reserving problems with full work shown.

Day 7

Re-do flagged problems and rebuild the loss reserving summary.

How exclam.ai helps you master Loss Reserving

Flashcards from your manual

Upload your ACTEX Exam ASTAM digital edition, scanned ASM pages, TIA handouts, or your own notes. exclam.ai extracts the Loss Reserving sections and generates flashcards automatically, tuned to the exam traps above.

Worked-example drilling

Each per-objective approach above maps to a quiz template. exclam.ai re-surfaces missed items until you can recall both the setup and the key identity from cold.

FSRS spaced repetition

Because Loss Reserving is 20–30% of your exam, losing it during review costs you. FSRS brings it back at the optimal moment.

Loss Reserving in the Exam ASTAM context

SOA Exam ASTAM has 5 topic areas. Loss Reserving is weighted at approximately 20–30% of the exam, here is where it sits relative to the other topics.

Topic areaWeight
Advanced Loss Modeling20–30%
Credibility Theory15–25%
Ratemaking15–25%
→ Loss Reserving20–30%
Reinsurance10–20%

Other Exam ASTAM topics

Advanced Loss Modeling

20–30%

Advanced severity, frequency, and aggregate loss models including tail fitting, censoring, and truncation.

Study this topic

Credibility Theory

15–25%

Classical limited fluctuation credibility, Buhlmann and Buhlmann-Straub models, and Bayesian credibility.

Study this topic

Ratemaking

15–25%

Loss ratio and pure premium methods, trend and development, expense provisions, and classification ratemaking.

Study this topic

Reinsurance

10–20%

Reinsurance structures including proportional and non-proportional treaties, and pricing reinsurance programs.

Study this topic

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