Choosing The Origin Period

Why the Origin Period Matters

A loss triangle organizes claim experience into rows and columns. The origin period defines the rows: it specifies which claims belong together before their development is observed. The same claim can therefore appear in different rows under different origin conventions. Choosing the wrong convention can make a triangle answer a different question from the one intended.

In this tutorial, examples use hypothetical claim records and deterministic dates and amounts. No interest rate, mortality assumption, or probability distribution is needed: the task is to classify records by a stated date rule. Amounts are used only to show how a row total changes when claims are grouped differently.

For calendar-year rows, a claim assigned to 2024 has its relevant origin date on or after January 1, 2024, and before January 1, 2025. This half-open interval convention gives a clear rule for dates on boundaries: an event on January 1 belongs to the new year, not the year that just ended. The same principle applies to other period lengths when their boundaries are specified.

The origin date is not the date at which the insurer observes or values the triangle. A claim may be assigned to an earlier origin period and reported later. The row continues to be determined by the chosen origin basis; later reporting does not change its original accident date or policy inception date.

Three Common Row Definitions

A policy-period convention needs particular care. In this tutorial, “policy year” means the calendar year containing the policy’s inception date. A claim arising during the policy term is assigned to that policy’s inception year, even if the loss occurs in a later calendar year. If a problem specifies a different policy-period convention, follow that definition instead.

The three dates can differ. For example, a loss can occur late in one year, be reported early in the next, and be covered by a policy that began in an even earlier year. No one date is universally the correct origin date; the intended row definition determines which date to use.

Assigning Claims to Rows

A reliable classification method is to identify the requested basis first, record its corresponding date for each claim, and then place that date in exactly one origin interval. Only after the row assignments are complete should claim counts or amounts be totalled. This avoids letting a memorable date, such as the report date, substitute for the date actually required by the row definition.

Policy Periods Can Cross Calendar Years

A policy-period row is based on policy inception, not the accident date and not the report date. Consequently, a policy-year row can contain claims from multiple accident years, and claims arising in the same accident year can be spread across different policy-year rows.

Why the Row Rule Produces a Consistent Partition

The logic of row assignment can be stated precisely. Let \(c\) denote a claim, and let \(g(c)\) be the date selected by the origin convention. For accident-period rows, \(g(c)\) is the accident date; for policy-period rows, it is the policy inception date; for report-period rows, it is the first report date. If the origin intervals are consecutive, nonoverlapping intervals that cover the dates under consideration, each claim’s selected date belongs to exactly one interval.

Thus the sets \(O_j\) are disjoint: if a claim belonged to two rows, its one selected date would have to lie in two nonoverlapping intervals, which is impossible. They also cover all the claims whose selected dates fall within the intervals. A row total, such as an amount total, is then formed from the claims in that set:

Here \(x_c\) is the claim amount being aggregated for the exercise. The row definition determines which claims enter \(T_j\); it does not by itself specify what measure of claim amount should be used. A triangle’s particular loss measure and observation structure must also be defined, but those choices do not change the origin-date rule.

Choosing and Stating the Basis

The appropriate origin basis depends on the intended analysis and the data available. Accident-period rows associate experience with when insured events occurred. Policy-period rows associate experience with policies according to their inception dates. Report-period rows associate experience with when claims entered the insurer’s reporting system. These are different organizing principles, not alternative labels for the same rows.

A useful exam habit is to state the rule in words before doing any calculation: “Each claim is assigned to the calendar year of its accident date,” for example. Then identify the date column that implements the rule. If the problem asks for report-year rows, a claim’s occurrence date may be relevant background, but it does not determine its row.

Common Mistakes and Exam Traps

• Using the wrong date. A report date does not determine an accident-year row, and an accident date does not determine a policy-year row.
• Ignoring policy inception. For policy-year rows as defined here, a claim occurring in 2025 can belong to a 2024 row if its covering policy began in 2024.
• Misclassifying a boundary date. Under calendar-year intervals beginning January 1, an event on January 1 belongs to the new year.
• Changing a claim’s origin after reporting. A delayed report changes the report-year assignment, but not the accident-year or policy-year assignment.
• Comparing totals without checking scope. When the same complete records are grouped under different bases, the overall amount should agree even though row totals differ. A mismatch can indicate an omitted or duplicated claim.