Estimating Claim Liabilities
Estimating Claim Liabilities
Estimating Claim Liabilities tests the actuarial estimate of unpaid claims: case reserves, IBNR, ultimate losses, development patterns, expected-loss methods, ULAE, discounting, and tail. You must choose a method that matches data maturity and explain why it is reasonable.
Core rules
- Ultimate = paid + case + IBNR. IBNR is the provision for claims not yet reported plus development on known claims; do not confuse it with case reserves.
- Development triangles give age-to-age factors and age-to-ultimate factors (CDFs). Chain-ladder applies CDFs to reported or paid losses, but it is sensitive to case-reserve strength and large claims.
- Expected-loss methods set ultimate from an expected loss ratio or expected claim count times severity. Bornhuetter-Ferguson (BF) blends expected ultimate with reported experience: IBNR = expected ultimate x (1 - percent reported). Cape Cod derives the expected loss ratio from the experience itself.
- Frequency-severity separates claim count development from severity development and is useful when counts and averages behave differently.
- ULAE covers claim-handling costs not assigned to individual claims; it can be added as a percentage of ultimate or via a paid/incurred mix.
- Claims-made exposures need report-year and maturity analysis; occurrence coverage needs accident-year and tail beyond the observed triangle.
Worked example
Reported losses at 24 months are 4,000,000; the 24-to-ultimate factor is 1.25, so the chain-ladder ultimate is 5,000,000 and IBNR is 1,000,000. The expected ultimate loss ratio is 65% on earned premium of 8,000,000, giving expected ultimate 5,200,000. Percent reported is 1/1.25 = 80%. BF IBNR = 5,200,000 x (1 - 0.80) = 1,040,000, so BF ultimate is 5,040,000. BF gives more weight to the expected loss ratio when the triangle is immature; chain-ladder gives full weight to observed development.
Traps
- Applying a paid CDF to incurred losses, or using a CDF that reflects a different case-reserve philosophy.
- Ignoring changes in case strength, claims handling, retention, or mix that distort development.
- Forgetting the tail beyond the triangle and ULAE.
- Using BF without a credible expected loss ratio, or using reported-to-date as the BF base instead of expected ultimate.
- Treating negative IBNR as automatically wrong; it can arise from redundant case reserves, but it needs explanation.
- Discounting without matching the payout pattern and risk margin.