Reserving and Claims Analysis
Reserving questions ask for a defensible central estimate, a range, and a story about what drives the difference. The examiner wants the method chosen to fit the data, not the data fitted to a familiar method.
The reserve build-up
- Unearned premium: UPR on a 365ths or 1/24ths basis, with acquisition costs treated consistently (DAC).
- Outstanding claims: case estimates plus a bulk IBNR for claims incurred but not reported and for case under-estimation (IBNER).
- ULAE: claims handling costs, split between fixed and allocatable.
- Discounting and inflation: discount only where the liability timing is genuinely predictable, and align claims inflation with the assumed investment return.
Choice of method
Chain ladder (development factors) suits mature, stable triangles. Bornhuetter–Ferguson blends reported claims with an expected loss ratio and is far safer for the most recent, immature year. Cape Cod derives the expected loss ratio from the data itself. Frequency-severity and case-estimate methods help where development is distorted. Mack gives a standard error for the chain-ladder estimate - useful for the range, but it captures process variance only, not parameter or model risk.
Worked example
Cumulative paid triangle (₹ lakh): AY2024 = 130; AY2023 = 120, 180; AY2022 = 110, 168, 182; AY2021 = 100, 150, 165, 170. Development factors: 1→2 ≈ 1.500; 2→3 ≈ 1.092; 3→4 ≈ 1.030.
- AY2024 ultimate = 130 × 1.500 × 1.092 × 1.030 ≈ ₹219.3 lakh, reserve ≈ ₹89.3 lakh.
- AY2023 ultimate = 180 × 1.092 × 1.030 ≈ ₹202.5 lakh, reserve ≈ ₹22.5 lakh. Total ≈ ₹111.8 lakh. Cross-check the latest year with a Bornhuetter–Ferguson estimate and widen the range if the two diverge.
Traps
Applying chain ladder to a very immature year; letting one large claim set the development factor; ignoring a change in settlement speed or case-reserving philosophy; presenting a single number with no range.