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

An insurer has an accident year with cumulative incurred claims of Rs 40 crore, and a development factor to ultimate of 1.6 (so 62.5% developed). The a priori loss ratio is 70% on earned premium of Rs 100 crore. Which statement is correct?

The BF ultimate is Rs 66.25 crore, above the chain ladder figure of Rs 64 crore. Chain ladder is 40 times 1.6, and BF is 40 plus 37.5% of the Rs 70 crore a priori ultimate, which is 26.25.

  1. AThe BF ultimate is Rs 66.25 crore, above the chain ladder ultimate of Rs 64 croreCorrect
  2. BThe BF ultimate is Rs 64 crore, equal to the chain ladder ultimate
  3. CThe BF ultimate is Rs 66.25 crore, below the chain ladder ultimate of Rs 70 crore
  4. DThe BF ultimate is Rs 56.25 crore, below the chain ladder ultimate of Rs 64 crore
  5. The BF ultimate is Rs 70 crore, above the chain ladder ultimate of Rs 64 crore

Explanation

Chain ladder ultimate = 40 x 1.6 = 64. A priori ultimate = 0.70 x 100 = 70. BF = 40 + 0.375 x 70 = 40 + 26.25 = 66.25. This is above 64 because the a priori of 70 exceeds the chain ladder 64. Check: BF lies between 64 and 70 as a credibility-type blend.

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