Actuarial research / 2026

Insurance models.
Decisions under
uncertainty.

Two independent studies of motor loss costs and reserve uncertainty. Inspect the test evidence, find where calibration fails, and explore the assumptions behind a price.

1.82%

Lower pricing devianceBoosting versus calibrated GLM.
135,198 held-out policies.

83.7%

Coverage of 95% intervalsBoth reserve methods.
36 of 43 held-out entities.

French motor policies and U.S. net-paid reserve histories describe different populations. These are historical research comparisons. The evidence does not establish a deployable tariff, commercial savings or certified reserve adequacy.

A predictive gain, with calibration gaps.

A fixed boosted frequency–severity model improves the primary combined loss-cost score. Its severity component is worse, and important conditional errors remain.

Final test · frozen models

Selected for this research comparison: boosting The paired interval is below zero, meeting the prespecified selection rule.

Where does calibration hold?

Observed / predicted loss: 1 means aggregate agreement; above 1 means losses exceeded predictions. Bars use development-calibrated predictions.

Model

Group policies by

Ratio ≤ 1Ratio > 1Vertical guide at 1

These are descriptive, heavy-tail-sensitive groups. No group confidence intervals or fairness conclusions are implied. Risk-decile cutpoints were fixed using training predictions.

Combined annual-loss deviance ↓Tweedie, power 1.5

Aggregate observed / predictedFinal test; calibration held fixed

Keep the failure cases visible

Inspect group counts and ratios

Group-level final-test calibration
Group	Policies	Claims	O / P

Illustrative assumptions

From loss cost to a price index

Start with a hypothetical expected loss cost of 100. Explore how assumed loss inflation, expenses and margin change the required premium index. These inputs are not estimated from the study.

Loss-cost inflation0%

Expenses / premium25%

Target margin / premium5%

required premium index
base loss cost = 100

Loss Expense Margin

Premium index =
100 × (1 + loss inflation) / (1 − expense ratio − margin ratio)

Expenses and margin are shares of premium. This simplified identity omits fixed costs, capital, tax, reinsurance and demand response. It does not change the measured model results or calculate realized profit.

What the comparison measures

Exposure-weighted expected annual loss, evaluated on a held-out policy split. Dates are unavailable, so this is not a temporal test. Preprocessing uses training data; each model has one development-only loss calibration factor.

Inspect pricing aggregates ↗

More complex uncertainty did not win.

Compare Mack-normal intervals with a positive factor/process simulation. Both retain negative net increments within a declared positive-cumulative domain.

Finite lag-10 endpoint

Retain Mack as the transparent referenceThe primary 2007 test did not establish a lower 95% interval score for simulation. Retaining the reference does not establish that its uncertainty is adequate.

Nominal coverage versus observed coverage

The dashed line marks the selected nominal level. The filled bars show how often the interval actually included an entity’s subsequent net paid loss through development lag 10.

Valuation date

Nominal interval level

Normalized interval performance
Method	Score ↓	Width

Scores penalize wide intervals and misses. Score and width are divided by each entity’s latest observed total paid loss, then averaged equally across entities. They are dimensionless, not currency amounts.

Fixed decision rule

The 95% interval-score comparison

Simulation minus Mack; a lower score is better. The full paired 95% bootstrap interval must be below zero to select simulation. Changing the coverage display does not change that rule.

1,000 paired entity bootstraps. Corporate links and common calendar shocks can weaken the independence assumption. Finite simulation quantiles also carry Monte Carlo noise.

What was known at the valuation?

Select only paid-loss cells visible by the valuation date.
Determine history completeness and positive-cumulative eligibility using that information.
Fit both methods and freeze forecasts before scoring the later endpoint.
Keep the original 2007 cohort as the primary comparison.

The source was compiled later. This is a computational as-of backtest, not verified historical release-vintage availability. Tail factor 1 specifies the lag-10 target; it does not prove ultimate settlement.

Inspect reserve aggregates ↗

Follow the evidence

Data and scope

677,991 reconciled French motor policies and a separate CAS/S&P U.S. reserve panel. Raw observations and entity-level forecasts are excluded from this explorer.

Provenance & source restrictions ↗

Protocol and validation

Prespecified splits, finite model budgets and frozen calibration. Numerical and information-boundary tests accompany the comparison.

Read the fixed protocol ↗

Decision and limitations

The measured pricing gain, reserve undercoverage and conditional failures remain visible in the full interpretation.

Read the decision memo ↗

Insurance models.Decisions underuncertainty.

A predictive gain, with calibration gaps.

Where does calibration hold?

More complex uncertainty did not win.

Nominal coverage versus observed coverage

Data and scope

Protocol and validation

Decision and limitations

Insurance models.
Decisions under
uncertainty.