Revision as of 23:36, 20 October 2024 by Admin (Created page with "You are given: #Earned premium in CY1 was 500,000. #Earned premium growth through CY3 has been constant at 10% per year (compounded). #The expected loss ratio for AY1 is 40%. #As of December 31, CY3, the expected loss ratio has increased 3 percentage points each accident year #Selected incurred loss development factors are as follows: {| class = "table table-bordered" | 12 to 24 months | 1.25 |- | 24 to 36 months | 1.2 |- | 36 to 48 months | 1.1 |- | 48 to 60 month...")
ABy Admin
Oct 21'24
Exercise
You are given:
- Earned premium in CY1 was 500,000.
- Earned premium growth through CY3 has been constant at 10% per year (compounded).
- The expected loss ratio for AY1 is 40%.
- As of December 31, CY3, the expected loss ratio has increased 3 percentage points each accident year
- Selected incurred loss development factors are as follows:
| 12 to 24 months | 1.25 |
| 24 to 36 months | 1.2 |
| 36 to 48 months | 1.1 |
| 48 to 60 months | 1.07 |
| 60 to 72 months | 1.05 |
| 72 to ultimate | 1.000 |
Calculate the aggregate projected ultimate loss for accidents years 1-3 as of December 31, CY3 using the Bornhuetter-Ferguson method.
ABy Admin
Oct 22'24
Solution: A
We compute:
| Year | Earned Premium | Expected Loss Ratio | Expected Loss | Cumulative Development Factor | Reserve |
|---|---|---|---|---|---|
| AY1 | 500,000 | 0.4 | 200,000 | 1.1 * 1.07 * 1.05 = 1.2356 | (1-1/1.2356) * 200,000 = 38,135.32 |
| AY2 | 550,000 | 0.43 | 236,500 | 1.2 * 1.1 * 1.07 * 1.05 = 1.483 | (1-1/1.483) * 236,500 = 77,025.96 |
| AY3 | 605,000 | 0.46 | 278,300 | 1.25 * 1.2 * 1.1 * 1.07 * 1.05 = 1.8534 | (1-1/1.8534) * 278,300 = 128,143.5 |
| Total: 243,305 |