Machine-led reserving method selection
Backtests chain-ladder, Bornhuetter–Ferguson, Benktander and Cape Cod on real Schedule P triangles by leave-diagonals-out hindsight, converts errors to Bayesian model weights and recommends a blended reserve.
Recommended method
Chain-ladder (simple average)
Blended reserve ($000)
18,731,582
Mack total CV
13.1%
Latest diagonal
34,358,090
Model weights and backtest error
| Method | Reserve | Ultimate | RMSLE | Bias | Cells | Weight |
|---|---|---|---|---|---|---|
| Chain-ladder (volume-weighted) | 18,680,856 | 53,038,946 | 8.1% | -0.5% | 24 | 25% |
| Chain-ladder (simple average) Recommended | 18,883,073 | 53,241,163 | 8.1% | -0.0% | 24 | 26% |
| Chain-ladder (last 3 diagonals) | 18,030,810 | 52,388,900 | 9.7% | -0.5% | 24 | 0% |
| Bornhuetter–Ferguson | 18,680,856 | 53,038,946 | 8.1% | -0.5% | 24 | 25% |
| Benktander (iterated BF) | 18,680,856 | 53,038,946 | 8.1% | -0.5% | 24 | 25% |
| Weighted blend | 18,731,582 | 53,089,672 | ||||
Why this recommendation
- Chain-ladder (simple average) minimises hindsight error (RMSLE 8.1%, bias -0.0%) over 24 backtested cells and receives 26% of the model weight.
- Mack total CV is 13.1%; the chain-ladder pattern is stable, so development methods are credible.
- Early age-to-age factors are stable (CV ≤ 25%).
- Blended reserve 18,731,582 vs. best single method 18,883,073; the blend hedges model risk (ASOP 43 §3.6.4).
Age-to-age factor CV by age: 1→2: 19% · 2→3: 10% · 3→4: 10% · 4→5: 6% · 5→6: 6% · 6→7: 4% · 7→8: 1% · 8→9: 2% · 9→10: 0%
Assumptions & limitations
- Backtests use only diagonals observed at the time; Cape Cod requires earned premium and is dropped when the dataset lacks it.
- Pseudo-BMA weights assume Gaussian log-errors with equal prior on methods; they measure short-horizon predictive accuracy, not tail adequacy.
- A credentialed actuary must still select and document the method (ASOP 43); this tool ranks candidates and quantifies model risk.