Why Use Report Year as the Origin Period?
A loss triangle’s origin period groups claims according to a chosen date. For a report-year triangle, the grouping date is when the insurer first receives notice of the claim. This differs from an accident-year triangle, which groups by when the loss occurred, and a policy-year triangle, which groups by the policy period’s start. The choice matters because the same claim can belong to a different row under each definition.
Report year is useful when the data question concerns claims entering the insurer’s reported claim system. A claim that occurred in one year but was first reported later belongs to the later report-year row. It does not move to another report-year row when it is paid, reopened, or otherwise develops; later transactions remain associated with its original report-year cohort under the stated data convention.
The report date must be defined consistently. In practice, a data extract may contain several dates, such as date of loss, date reported by the insured, date received by the insurer, and date entered into a system. For a report-year triangle, use the specified first-report date—not whichever date happens to be easiest to retrieve. If the source data records late, a system-entry date may not equal the actual date the insurer received notice.
Assigning Claims to Report-Year Rows
To determine row membership, identify each claim’s first-report date and take its calendar year. Do not substitute the accident date, policy effective date, or payment date. A payment made years after first report remains attached to the same report-year claim.
Use the first-report date specified for the data, and confirm how the source treats a claim with multiple date fields.
Place the claim in the calendar-year row containing that first-report date.
Group the claim’s payments or incurred amounts with its report-year cohort, then measure them at the triangle’s stated valuation dates and development ages.
Verify that a claim reported after year-end is not included in the earlier report-year row merely because its accident occurred then.
Worked Example: Assigning Claims When Dates Differ
A hypothetical insurer is preparing annual report-year rows. For this example, report year is the calendar year of the first notice received by the insurer. Assign each claim below to a report year, and distinguish that assignment from its accident and policy years.
Claim A: The policy began July 1, 2022. The accident occurred February 10, 2023, and the insurer first received notice January 8, 2024.
Claim B: The policy began April 1, 2023. The accident occurred December 28, 2023, and first notice was received December 30, 2023.
Claim C: The accident occurred December 31, 2022, and first notice was received January 2, 2023.
Claim D: The accident occurred August 14, 2023, and first notice was received August 20, 2023.
Method. Use the first-report date for the report-year row; use the accident date only to identify accident year. A policy year, when relevant, is identified from the policy period rather than either of those dates.
Claim A: First notice is January 8, 2024, so Claim A belongs in report year 2024. Its accident year is 2023, and its policy began in 2022.
Claim B: First notice is December 30, 2023, so Claim B belongs in report year 2023. Its accident year is also 2023, and its policy began in 2023.
Claim C: First notice is January 2, 2023, so Claim C belongs in report year 2023, even though the accident was in 2022.
Claim D: First notice is August 20, 2023, so Claim D belongs in report year 2023; its accident year is also 2023.
Check. The report-year 2023 row contains Claims B, C, and D: three claims. The report-year 2024 row contains Claim A: one claim. The trap avoided is assigning Claim C to 2022 because its accident occurred then, or assigning Claim A to 2023 because its accident occurred then.
Building Annual Rows and Their Development Ages
For an annual triangle, the age convention must specify the valuation dates associated with each age. One common convention labels the first year-end after the report year as age 12 months, the next as age 24 months, and so on. Under this convention, a report-year 2022 row has ages 12, 24, and 36 months at December 31, 2022, 2023, and 2024, respectively. The convention is an aggregate approximation: claims reported at different points within the year do not each have exactly the same elapsed time since report at year-end.
For a cumulative paid triangle, each cell is the sum of eligible payments on claims in the row through the cell’s valuation date. A blank cell for a valuation date not yet reached is not a zero; it means that observation is unavailable at that valuation. The rule for claim membership stays the same whether the triangle measures paid or incurred amounts, although the amount being accumulated or recorded differs.
Worked Example: Constructing Cumulative Paid Report-Year Rows
A hypothetical insurer uses the annual convention above and records the following payments, all in thousands of dollars. Claim A was first reported in February 2022 and received payments of $4 in April 2022, $2 in April 2023, and $1 in April 2024. Claim B was first reported in November 2022 and received payments of $3 in December 2022 and $2 in August 2023. Claim C was first reported in March 2023 and received a payment of $5 in May 2023. Claim D was first reported in December 2023 and received payments of $2 in December 2023 and $1 in June 2024. Construct the cumulative paid cells at ages 12, 24, and 36 months where available.
Method. First group claims by first-report year. Then, for each age, sum payments through that row’s valuation date. The common mistake avoided is grouping payments by the calendar year they were made rather than keeping each payment with its claim’s report-year row.
Report-year 2022, age 12. The valuation date is December 31, 2022. Claim A has $4 paid by then; Claim B has $3. Thus the cell is \(4+3=7\) thousand dollars.
Report-year 2022, age 24. The valuation date is December 31, 2023. Claim A’s cumulative paid amount is \(4+2=6\); Claim B’s is \(3+2=5\). The cell is \(6+5=11\) thousand dollars.
Report-year 2022, age 36. The valuation date is December 31, 2024. Claim A’s cumulative amount is \(4+2+1=7\); Claim B’s remains \(3+2=5\). The cell is \(7+5=12\) thousand dollars.
Report-year 2023, age 12. The valuation date is December 31, 2023. Claim C has $5 paid by then; Claim D has $2. The cell is \(5+2=7\) thousand dollars.
Report-year 2023, age 24. The valuation date is December 31, 2024. Claim C remains at $5, and Claim D’s cumulative paid amount is \(2+1=3\). The cell is \(5+3=8\) thousand dollars. The age-36 cell is not yet observable at December 31, 2024.
| Report year | Age 12 months | Age 24 months | Age 36 months |
|---|---|---|---|
| 2022 | 7 | 11 | 12 |
| 2023 | 7 | 8 | Not yet observable |
Check. Every cell is cumulative, so the 2022 values satisfy \(7 \leq 11 \leq 12\), and the 2023 values satisfy \(7 \leq 8\). The payments made in 2023 on 2022-reported claims increase the 2022 row, not the 2023 row.
Why Reporting Delays Change the Row Mix
A reporting delay is the time between the event that produced a claim and the insurer’s first report of it. Under report-year grouping, a delay changes the claim’s row assignment: an accident in one year may appear in a later report-year row. Thus report-year rows do not represent a fixed set of accident years. A row can combine claims from several accident years, while an accident-year cohort can be spread across multiple report years.
This follows directly from the membership rule. Let \(R(c)\) be the calendar year of claim \(c\)’s first report, and let \(I\{R(c)=r\}\) equal 1 when the claim was first reported in year \(r\), and 0 otherwise. The number of claims in report-year row \(r\) is the sum of these membership indicators. A delayed claim contributes to the row of its report date because that is the year for which its indicator equals 1.
The same logic applies to a paid amount at a valuation date: include the claim’s payment in the row selected by its first-report year, provided the payment falls on or before that cell’s valuation date. The calendar year in which the payment occurs determines which valuation includes it, not which origin row receives it.
Worked Example: A Delayed Claim Enters a Later Report-Year Row
Consider three hypothetical claims in a report-year triangle valued at December 31, 2023. Claim P arose from an accident on November 20, 2021, was first reported February 5, 2023, and had $9,000 paid by December 31, 2023. Claim Q arose from an accident on September 10, 2023, was first reported September 15, 2023, and had $4,000 paid by year-end. Claim R arose from an accident on December 20, 2022, was first reported December 28, 2022, and had $6,000 paid on March 15, 2023.
Method. Assign each claim using first report, then apply the annual age convention. Claim P’s delay is more than a year, but it is still assigned to the year it was reported. The trap avoided is placing its $9,000 in the 2021 accident-year row of a report-year triangle.
Claim P: First report was in 2023, so it belongs to report year 2023. At age 12 months, its $9,000 paid by December 31, 2023, is included.
Claim Q: First report was also in 2023, so it belongs to report year 2023. Its $4,000 paid by year-end is also included at age 12 months.
Claim R: First report was in 2022, so it belongs to report year 2022. Its payment in March 2023 is included in that row at age 24 months, not in the 2023 row. At the age-12 valuation date of December 31, 2022, no payment had yet been made on Claim R, so its contribution at that age is zero.
Result and check. The report-year 2023 age-12 paid amount is \(9{,}000+4{,}000=13{,}000\) dollars. The report-year 2022 age-24 paid amount is \(6{,}000\) dollars, while its age-12 paid amount is \(0\). Each payment is counted once, in the row determined by its claim’s first-report year. The two claims in the 2023 row arose in different accident years, illustrating how reporting delays change the row mix.
Common Mistakes and Practical Checks
Report-year triangles answer questions about claims grouped by when they were first reported; they do not, by themselves, identify when the underlying losses occurred. Interpretation should keep that purpose in view. A change in the number or amount of claims appearing in a report-year row may reflect changes in underlying losses, reporting speed, or both.
- Using accident year by mistake. A claim reported in 2024 for a 2022 accident belongs to report year 2024, not report year 2022.
- Using payment year as origin. A 2023 payment on a claim reported in 2022 remains in the 2022 row.
- Changing the first-report definition across records. Mixing date received with date entered into a system can shift claims between rows.
- Comparing rows as if their claim mix were identical. Reporting delays can make a later report-year row contain older accidents than an earlier row.
- Treating an unobserved cell as zero. If the valuation date has not occurred, the cell is not yet observable; it is not evidence of no payments.
A useful validation is to select a sample of claims and trace each from its first-report date through its transactions. Confirm that the claim appears in one report-year cohort, that later payments stay attached to that cohort, and that each cumulative cell includes only transactions through its valuation date. These checks do not eliminate reporting delays, but they help ensure that the triangle represents its stated origin-period definition.
Check Your Understanding
For each problem, use the stated report-year definition and annual age convention.
- A claim occurred on December 29, 2024, and was first reported on January 3, 2025. Which report-year row contains it? (Answer: 2025)
- Two claims were first reported in 2022. Claim A had $2,400 paid by December 31, 2022, and another $600 paid in 2023. Claim B had $1,000 paid in 2022 and $500 in 2023. What are the combined cumulative paid amounts at ages 12 and 24 months? (Answer: $3,400 at age 12 months and $4,500 at age 24 months)
- A claim was first reported in October 2023 and paid $1,200 in December 2023 and $800 in February 2024. Under the stated convention, what is its cumulative paid amount in the report-year 2023 row at ages 12 and 24 months? (Answer: $1,200 at age 12 months and $2,000 at age 24 months)
- Claim M occurred in 2021 and was first reported in 2023; Claim N occurred in 2022 and was first reported in 2023. Each had $3,000 paid by December 31, 2023. What is the report-year 2023 age-12 cumulative paid amount, and how many accident years are represented? (Answer: $6,000; two accident years)
- A report-year 2022 cohort has $5,000 paid through December 31, 2022. A further $2,000 is paid in March 2023 on a claim in that cohort. What are the cumulative paid amounts at ages 12 and 24 months, and which row includes the March payment? (Answer: $5,000 at age 12 months and $7,000 at age 24 months; the report-year 2022 row)