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.

00