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

In the basic chain ladder method applied to a cumulative claims run-off triangle, which of the following best describes how the development factor from development year j to j+1 is usually estimated?

The development factor is the sum of cumulative claims at development year j+1 divided by the sum of cumulative claims at year j, using only accident years where both values are observed. This gives a volume-weighted ratio that is applied to the latest cumulative claims.

  1. AThe simple average of the incremental claims in year j+1 divided by the average incremental claims in year j
  2. BThe sum of cumulative claims at j+1 divided by the sum of cumulative claims at j, over the accident years where both are observedCorrect
  3. CThe ratio of the latest diagonal to the first column of the triangle
  4. DThe sum of cumulative claims at j+1 divided by the sum of cumulative claims at j, over all accident years including those with no data at j+1
  5. The ratio of ultimate claims to the total premium earned in the accident year

Explanation

The volume-weighted chain ladder factor sums cumulative claims at j+1 and at j only over accident years where both are observed. Including years without a j+1 value (option 3) would understate the factor because the denominator would contain claims with no matching numerator.

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