How to Count Claims That Have Not Been Reported Yet

In one line

There are accidents that have already happened but have not yet been reported, and their amount can be computed if you know the reporting lag distribution, and if you do not compute it, the reserve falls short by that much.

Why this was needed

The person in charge of the close asks this: "The June accident count comes out as 55. Is that right?"

You look at the data. The cases reported as June accidents are exactly 55. The query is right and the join is right. But May is 160 and April is 90. Only June is conspicuously low.

If you answer "there were few accidents in June," you are wrong. It is because among the June accidents there are some not yet reported. The closing date is June 30, so an accident on June 25 has not yet had time for the documents to come in.

How it works

It takes time from an accident happening to its being reported. It takes several days to several months to visit the hospital, get the documents, and contact the company. Because of this lag, the data at closing time is always not yet fully developed.

If you make this into a table, a triangle comes out.

사고월      접수 지연 0개월  1개월  2개월  3개월  4개월  5개월
2025-07          55      25     10      6      3      1     ← 다 자랐다
2025-08          55      25     10      6      3      1
  …
2026-04          55      25     10      ·      ·      ·     ← 아직 자라는 중
2026-05         110      50      ·      ·      ·      ·
2026-06          55       ·      ·      ·      ·      ·     ← 이제 막 시작

The empty lower right is not data missing but time that has not yet passed. This table is called a development triangle.

Now the calculation comes out. You gather only the fully developed accident months and extract the cumulative reporting rate.

지연 0개월까지 누적   55%
     1개월까지        80%
     2개월까지        90%
     3개월까지        96%
     4개월까지        99%
     5개월까지       100%

The 2026-06 accident month has been observed only up to lag 0 months, so the 55 cases you see now are 55% of the final. The final is 100 cases, and 45 have not yet come. These 45 cases are IBNR (Incurred But Not Reported). They are cases that have already had an accident but have not yet been reported.

The reserve has two pieces.

미지급 발생손해   이미 접수된 건 중 아직 안 나간 돈 (발생손해액 − 기지급액)
IBNR 추정액       아직 접수도 안 된 건에 나갈 돈 (추정 건수 × 건당 평균)

A trap comes out in the second piece. It is how you take the average per case. If a single large accident is mixed in, the average jumps up, and if you compute the IBNR estimate from that average, the reserve is inflated from tens of millions of won to hundreds of millions. The usual treatment is to set large cases apart and estimate them individually, leaving them out of the average.

Under-booking and over-booking have different consequences. Under-booking inflates that year's profit and pops out as a loss the next year when the actual claims come in. Regulators take this seriously. Over-booking ties up capital unnecessarily and pushes up product prices. Both are wrong, but the regulatory risk is far greater for the former.

What it looks like in the field

First, be careful with reports in which recent months look good. If this month's loss ratio on a loss ratio dashboard looks like it dropped sharply, IBNR has usually not been added. Next month it returns to its original place, and then a meeting is held asking "why did it suddenly get worse?"

Second, when extracting ratios, you must not mix in months that are still developing. If you draw the conclusion "most accidents are reported in the month they occur" from all the data, the fact that cases that will arrive late for recent months have not yet come hardens into a statistic. You must use only fully developed months.

Third, IBNR is produced by the actuarial department with sophisticated models. An FDE will never replace that model. But you must be able to explain "why is this number like this." Merely counting the lag distribution can tell you whether it is a data problem or a calculation problem, and that is the depth needed in the field.

What you will do in the lab that follows

First, the next reading covers reinsurance cessions, and then you move on to the lab.

You build 1,296 losses and set up the triangle by accident month and reporting lag. From the 7 fully developed months you extract the cumulative reporting rate, estimate the final counts for the five months still developing, and find the 104 unreported cases. Then you compute the reserve in two pieces, computing side by side the two versions in which a large case is put in or left out of the per-case average, and see the 96,062,824 won by which they split.