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IAI Actuarial Core Principles · Economic Modelling · Run-off triangles

In a cumulative run-off triangle of paid claims, rows are accident years and columns are development years. Which statement best describes what the triangle contains?

A run-off triangle holds observed past claim data, such as paid amounts, arranged by accident year and development period. Only the upper-left cells are known, so the shape is a triangle. The missing lower-right cells are the future values that reserving methods aim to estimate.

  1. AOnly the future payments expected for each accident year
  2. BClaim amounts for past accident years observed at each development period so far, forming the upper-left part of a squareCorrect
  3. CPremiums earned for each underwriting year by development period
  4. DReported claim counts for future accident years only
  5. Reserves held at each year-end after discounting

Explanation

A run-off triangle records observed claim data (paid or incurred, amounts or counts) by accident year and development period. Only the cells already observed are filled, giving a triangle shape; the unfilled lower-right part is what methods try to project. Future payments are not in the triangle.

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