The question behind this project
How much will an insurer still need to pay?
An accident happens today, but its bills can arrive for years. We look at past payments to estimate how much money an insurer needs to set aside for what comes next.
Read the analysis
Insurance An analytical case study
Estimating outstanding insurance claim payments
How much remains to be paid, and how sensitive is that estimate to the reserving method?
The finding
The newest accident years contain the least observed development. Their ultimate cost depends most on the projection assumptions.
Analytical work
Translate loss triangles into an explanation of unpaid obligations, model sensitivity, and profitability assumptions.
Claims payments made and estimated payments remaining
Development period →
of projected ultimate losses already paid
1997 · 1 observed periods01
Read across one accident year
A row groups claims from the same accident year. Moving right adds development time, not new accident years. At the valuation date, the missing corner is unobserved future development; it is not zero loss.
02
Separate what is paid from what is estimated
Paid losses are cash already disbursed. Incurred losses include paid amounts and case reserves. Ultimate losses are projected final costs. Ultimate minus paid is the total unpaid reserve; ultimate minus incurred is the additional provision beyond reported losses.
03
Compare the assumptions, then the estimates
Chain-ladder extends observed development patterns. Bornhuetter–Ferguson combines emergence patterns with an a priori expected loss ratio, giving immature years another anchor. Their difference is model sensitivity, not a confidence interval.
Decision supported
What to do with this evidence
Review the immature years and long-tail lines before using a point estimate for reserve or pricing discussions. Compare methods on the same paid or incurred basis.
What this analysis cannot establish
- Claim-level severity, frequency, and reporting delays are synthetic demonstrations calibrated to aggregates; they are not observed policyholder records.
- Combined ratios assume a 30% expense ratio. Profitability conclusions change with that assumption; no stochastic reserve interval is estimated.
Continue the investigation