Claims Development and Reserving
Claims Development and Reserving
Reserving estimates the future cost of events that have already occurred. A run-off triangle is a data arrangement, not a method: rows identify origin periods, columns identify development age, and diagonals identify calendar periods.
1. Fix the data contract
Before calculating a factor, document:
| Question | Harbour Mutual answer | Why it matters |
|---|---|---|
| What is one row? | accident year | policy year and report year answer different questions |
| What is one column? | annual development age | unequal intervals invalidate a simple factor comparison |
| Incremental or cumulative? | cumulative paid loss | link ratios require a consistent basis |
| Gross or net? | gross of reinsurance | mixing bases changes development mechanically |
| Currency and price level? | nominal £m | inflation can create calendar effects |
| Information date? | 31 December 2023 | determines which cells were genuinely observable |
| What is “ultimate”? | selected value after Dev 3 | oldest observed does not automatically mean complete |
2. See all three time axes
For origin year , development age , calendar year is . Therefore cells on a diagonal share an economic and operational period.
| AY | Dev 0 | Dev 1 | Dev 2 | Dev 3 |
|---|---|---|---|---|
| 2020 | 100 | 180 | 240 | 280 |
| 2021 | 120 | 220 | 300 | — |
| 2022 | 140 | 260 | — | — |
| 2023 | 160 | — | — | — |
The bold diagonal is the latest observation. A claims-system change in calendar 2023 can affect all four bold cells, even though they have different development ages. A pure development model may mistake that diagonal effect for ordinary maturation.
3. Convert carefully
If is incremental loss and cumulative loss,
For AY 2020, cumulative becomes incremental . Negative paid increments usually indicate recoveries, corrections, or data errors; negative incurred increments can also reflect case-reserve releases. Investigate rather than deleting them automatically.
4. Diagnose before modelling
Use this order:
- Reconcile triangle totals to the source system or ledger.
- Check duplicates, currencies, gross/net basis, and reopenings.
- Plot age-to-age factors by origin year.
- Plot incremental proportions by development age.
- Inspect calendar diagonals for inflation, legislation, operational changes, or catastrophes.
- Separate large losses or materially different claim types when justified.
- Record every adjustment and retain an unmodified extract.
Mini-case: faster settlement or lower severity?
Suppose Dev-0 paid loss rises from 140 to 160 while ultimate claim cost is unchanged. A chain ladder may interpret the higher early payment as a higher ultimate. An operational explanation—claims are being settled earlier—implies a lower later factor instead. Paid triangles cannot distinguish these explanations without claim counts, incurred data, or operational evidence.
5. Choose the question, then the method
| Method | Main evidence | Useful when | Main vulnerability |
|---|---|---|---|
| Chain ladder | observed development pattern | triangle is sufficiently mature and stable | recent years inherit historical pattern |
| Frequency–severity | count emergence and average cost | count and cost processes explain the movement | inconsistent count definitions; interaction between processes |
| Bornhuetter–Ferguson | prior ultimate plus observed maturity | immature periods need external structure | prior may be weak or stale |
| Uncertainty and diagnostics | residuals, backtests, stochastic assumptions | a point reserve is not enough | assumptions can be hidden behind one error number |
These are not competing buttons. A reserve committee compares their evidence, understands differences, and selects a range or central estimate.
Practice: classify the problem
For each observation, identify the most relevant axis and one response.
- All claim types settle faster after a new payment platform goes live in 2022.
- Bodily-injury claims have much larger and later payments than vehicle-damage claims.
- One catastrophe affects several origin years through reopened claims in the same calendar year.
- A recent year has almost no development data, but pricing supplied an expected loss ratio.
Suggested answers
- Calendar/operational effect: inspect diagonals and paid-versus-reported speed; do not extrapolate old link ratios blindly.
- Portfolio heterogeneity: segment if definitions and volume support it.
- Calendar/event effect: isolate and model the event where appropriate.
- Immaturity: BF or another prior-informed method may be more stable than chain ladder alone.
Public data for extended work
The Casualty Actuarial Society provides updated Schedule P loss-reserve data and associated research resources. They are useful for reproducing methods on real triangles, but Schedule P line definitions and US reporting conventions must be documented before transferring a conclusion to another market.