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

In practice, the latest diagonal of a triangle for a long-tailed liability class shows that all accident years have been fully developed to development year 5, but claims are known to continue beyond that. What is the appropriate way to deal with this under chain ladder?

The actuary should apply a tail factor greater than one, derived from external benchmark data or an extrapolated curve, to the latest cumulative claims. The triangle has no information beyond development year 5, so ignoring the tail would understate ultimate claims and reserves.

  1. ASet all future reserves to zero because the triangle is complete
  2. BUse only the first development year factor for all later periods
  3. CApply a tail factor greater than one, based on external data or a fitted curve, to the latest cumulative claimsCorrect
  4. DRemove the oldest accident year and recalculate all factors
  5. Replace cumulative claims with incurred claim counts

Explanation

A triangle only contains observed development; when claims continue beyond the last observed year, a tail factor above one, estimated from external benchmarks or an extrapolated curve, is needed to estimate ultimate claims. Setting reserves to zero would understate liabilities.

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