Actuarial case explained
Which claims cost has not yet emerged in observed payments?
Purpose
Decision informed
Select a central estimate and separately disclose development, tail, and uncertainty.
Benefits and cash flows
- 1Observed paid or incurred claims by origin and development.
- 2Future cells projected to ultimate.
- 3Reserve equals ultimate less observed.
Assumptions
| Assumption | Value / unit | Source and status |
|---|---|---|
| Triangle | Cumulative, MXN millions | Illustrative Reproducible 2019–2024 case |
| Pattern | Stable across origin years | Convention Chain Ladder assumption |
| Tail | Declared or Sherman | Convention Explicit extrapolation |
Method
Volume-weighted Chain Ladder
Factors develop each diagonal; Mack and ODP bootstrap quantify error conditional on the model.
Reserva = Σ(Ultimateᵢ − Observadoᵢ)Results and interpretation
The tail factor can materially move the reserve even though no observed cell identifies it by itself.
Applied example
The reserve and the tail factor
Claims from a given year generate payments over several years. To estimate the required reserve, the actuary projects a triangle of historical payments (2019-2024, MXN millions) with Chain Ladder. The tail factor represents development expected after the last observed period.
Adjust the parameters to observe how the result changes.
Estimated reserve
—
Estimated ultimate cost
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Actuarial interpretation
A 3% tail factor changes the reserve by several million pesos. Reserves are estimates that are sensitive to assumptions; regulation requires documenting them, and actuarial practice quantifies their uncertainty. The lab implements Mack's (1993) model, which estimates a variance per development period and composes the prediction error by origin year; it measures error conditional on Chain Ladder, not model risk.
Validation and limits
What is checked
- —Mack reproduces the Taylor and Ashe case to the currency unit.
- —The ODP bootstrap reproduces the published φ and reconciles with Chain Ladder.
What it does not prove
- —Mack and ODP do not cover model risk, mix change, or unobserved inflation.
- —Every tail is extrapolation and requires external justification.