One $4 million fire lands in a single accident year. If you leave it in the paid triangle, that year's development factor spikes, and the chain ladder projects a phantom pattern onto every other year. The fix is to pull the big claim out, develop the rest, and add the large losses back in on their own terms.
A loss triangle assumes each accident year develops along a similar percentage path. That works when claims are numerous and homogeneous. A single catastrophic claim violates the assumption. It inflates one cell, warps the age-to-age factor out of that cell, and because you average factors across years, it contaminates the projection for years that never had such a claim.
KEY: The goal is not to erase large losses. It is to stop one accident year's random big claim from setting the development pattern for all years.
You have two coequal ways to keep one big claim from steering the pattern. Both strip its volatile portion from the working triangle, then add a separately estimated large-claim provision back.
Common mistakes
- Removing a large claim without adding a provision back. Whether you cap the claim at the threshold or exclude it in its entirety, the removed cost is real liability. Both treatments are legitimate. The mistake is dropping the claim and stopping, which understates the reserve.
- Reporting an excess estimate below the reported excess. A provision under the excess already on the books implies negative excess IBNR, meaning you expect the reported large claim to shrink. Justify it (salvage, subrogation, documented overstatement) or raise the estimate.
- Using a flat nominal threshold across inflated years. A constant $500,000 over ten years caps older years at a higher real level, biasing the limited/excess split.
Bottom line
- Large losses are low-frequency, high-severity claims that emerge erratically and distort age-to-age factors if left in the raw triangle.
- Two coequal treatments: cap each claim at a large-loss threshold (excess to its own bucket) or exclude the whole large claim from the triangle; either way add a separately estimated large-claim provision back.
- Set the threshold high enough that few claims exceed it but low enough to strip the volatile tail; it must be consistent across all accident years, trended for inflation if stated in nominal dollars.
- Limited losses develop smoothly because the volatile excess portion is removed; their loss development factors are more stable and credible.
Exam shortcut
When a problem flags a specific large claim in a triangle, immediately handle it either way the data invites: split it at the stated threshold, or exclude it entirely, drop the excess out of the cell, and re-run the age-to-age factor to show the smoother pattern. Then add a large-claim provision back regardless of which treatment you chose. The threshold rule of thumb: same real dollar level every year.
The full lesson (about 2,348 words, 16 min read) adds 2 worked examples, all 7 common mistakes, a self-check, free in the app.
Learning objectives
- B12
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