Revision as of 21:28, 14 May 2023 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 Lo...")
ABy Admin
May 14'23
Exercise
| Cumulative Loss Payments through Development Month | ||||||
| Accident Year | Earned Premium | Expected Loss Ratio | 12 | 24 | 36 | 48 |
| AY5 | 19,000 | 0.90 | 4,850 | 9,700 | 14,100 | 16,200 |
| AY6 | 20,000 | 0.85 | 5,150 | 10,300 | 14,900 | |
| AY7 | 21,000 | 0.91 | 5,400 | 10,800 | ||
| AY8 | 22,000 | 0.88 | 7,200 | |||
There is no development past 48 months.
Calculate the indicated loss reserve using the Bornhuetter-Ferguson method and volume-weighted average loss development factors.
- 22,600
- 23,400
- 24,200
- 25,300
- 26,200
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
May 14'23
Key: B
The year-to-year development factors are 12-24: 30,800/15,400 = 2; 24-36: 29,000/20,000 = 1.45; and 36-48: 16,200/14,100 = 1.149. Then the factor for 24-48 is 1.45(1.149) = 1.666 and for 12-48 is 2(1.666) = 3.332.
The expected ultimate losses are AY6: 20,000(0.85) = 17,000; AY7: 21,000(0.91) = 19,110; and AY8: 22,000(0.88) = 19,360.
The B-F reserves are 17,000(1 – 1/1.149) = 2205, 19,110(1 – 1/1.666) = 7639, and 19,360(1 – 1/3.332) = 13,550.
The total is 23,394.