Revision as of 13:36, 21 October 2024 by Admin (Created page with "{| class = "table table-bordered" | <br> | <br> | <br> | colspan="4" | Cumulative Loss Payments through Development Month |- | Accident Year | Earned Premium | Expected Loss Ratio | 12 | 24 | 36 |- | AY1 | 9,500 | 0.7 | 5,250 | 6,700 | 7,500 |- | AY2 | 10,000 | 0.72 | 5,250 | 7,300 | <br> |- | AY3 | 11,500 | 0.75 | 6,550 | <br> | <br> |} There is no development past 36 months. Calculate the indicated loss reserve using the Bornhuetter-Ferguson method and volume-...")
Oct 21'24
Exercise
| Cumulative Loss Payments through Development Month | ||||||
| Accident Year | Earned Premium | Expected Loss Ratio | 12 | 24 | 36 | |
| AY1 | 9,500 | 0.7 | 5,250 | 6,700 | 7,500 | |
| AY2 | 10,000 | 0.72 | 5,250 | 7,300 | ||
| AY3 | 11,500 | 0.75 | 6,550 | |||
There is no development past 36 months.
Calculate the indicated loss reserve using the Bornhuetter-Ferguson method and volume-weighted average loss development factors.
Oct 22'24
Solution: B
Step 1: Calculate year-to-year development factors
| Months | Factor |
|---|---|
| 12-24 | (6,700 + 7,300)/(5,250 + 5,250) = 1.3333 |
| 24-36 | 7,500/6,700 = 1.1194 |
Step 2: Calculate expected losses for each accident year
| Accident Year | Expected Loss |
|---|---|
| AY2 | 10,000 *0.72 = 7,200 |
| AY3 | 11,500 * 0.75 = 8,625 |
Step 3: Calculate the reserves for each accident year using the Bornhuetter-Ferguson method
| Accident Year | Expected Loss | Cumulative Development Factor | Reserve |
|---|---|---|---|
| AY2 | 7,200 | 1.1194 | (1-1/1.1194)*7,200 = 767.98 |
| AY3 | 8,625 | 1.3333 * 1.1194 = 1.4925 | (1-1/1.4925)*8,625 = 2,846.11 |
| Total: 3,614.09 |