Exercise
You are given:
- An insurance company was formed to write workers compensation business in CY1.
- Earned premium in CY1 was 1,000,000.
- Earned premium growth through CY3 has been constant at 20% per year (compounded).
- The expected loss ratio for AY1 is 60%.
- As of December 31, CY3, the company’s reserving actuary believes the expected loss ratio has increased two percentage points each accident year since the company’s inception.
- Selected incurred loss development factors are as follows:
12 to 24 months | 1.500 |
24 to 36 months | 1.336 |
36 to 48 months | 1.126 |
48 to 60 months | 1.057 |
60 to 72 months | 1.050 |
72 to ultimate | 1.000 |
Calculate the total IBNR reserve as of December 31, CY3 using the Bornhuetter-Ferguson method.
- 964,000
- 966,000
- 968,000
- 970,000
- 972,000
Key: E
CY1: ELR = 60%, earned premium = 1,000,000, expected losses = 0.6(1,000,000) = 600,000. Cumulative development factor (CDF) = (1.05)(1.057)(1.126) = 1.250. Reserve using BF method = 600,000(1 – 1/1.250) = 120,000.
CY2: ELR = 62%, earned premium = 1,200,000, expected losses = 0.62(1,200,000) = 744,000. CDF = (1.05)(1.057)(1.126)(1.336) = 1.670. Reserve using BF method = 744,000(1 – 1/1.670) = 298,491.
CY3: ELR = 64%, earned premium = 1,440,000, expected losses = 0.64(1,440,000) =921,600. CDF = (1.05)(1.057)(1.126)(1.336)(1.5) = 2.504. Reserve using BF method = 921,600(1 – 1/2.504) = 553,549. Total reserve = 120,000 + 298,491 + 553,549 = 972,040.