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

The Bornhuetter-Ferguson ultimate can be written as Z times the chain ladder ultimate plus (1 - Z) times the a priori ultimate. If p is the proportion of ultimate developed to date, what is Z?

Z equals p, the proportion developed. Since claims to date equal p times the chain ladder ultimate, the BF ultimate is p times chain ladder plus (1 - p) times the a priori ultimate, so credibility rises as the year matures.

  1. AZ = 1 - p
  2. BZ = 1/p
  3. CZ = pCorrect
  4. DZ = p squared
  5. Z = 0.5 for all development years

Explanation

Let C be claims to date and U the a priori ultimate. BF = C + (1-p)U. Chain ladder = C/p, so C = p x CL. Then BF = p x CL + (1-p)U, so Z = p. As the year matures, p rises toward 1 and BF approaches the chain ladder.

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