IAI Actuarial Core Principles · Economic Modelling · Run-off triangles
For an immature accident year, cumulative incurred claims are Rs 40 lakh, the incurred development factor to ultimate is 2.0, premium is Rs 200 lakh and the prior loss ratio is 60%. What is the difference between the chain ladder ultimate and the Bornhuetter-Ferguson ultimate?
The difference is Rs 20 lakh. Chain ladder gives Rs 80 lakh, while Bornhuetter-Ferguson gives Rs 40 lakh plus half of the Rs 120 lakh prior ultimate, which is Rs 100 lakh, so BF is higher by Rs 20 lakh.
- ARs 20 lakhCorrect
- BRs 40 lakh
- CRs 10 lakh
- DRs 0
- Rs 30 lakh
Explanation
Chain ladder ultimate = 40 x 2 = 80. Expected ultimate = 0.6 x 200 = 120. Undeveloped proportion = 1 - 1/2 = 0.5, so BF = 40 + 0.5 x 120 = 100. Difference = 100 - 80 = 20.
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