An actuary is establishing reserves for a group of policies as of December 31, CY3. You are given the following table of reserve estimates for AY1 and AY2:

	Reserve estimates as of December 31, CY3
	[math]R_{BF}[/math]	[math]R_{LR}[/math]	[math]R_{CL}[/math]
AY1	400,000	250,000	437,500
AY2	1,120,000	1,200,000	1,050,000

where [math]R_{BF}[/math] is the loss reserve under the Bornhuetter-Ferguson method, [math]R_{LR}[/math] is the loss reserve under the Expected Loss Ratio method, and [math]R_{CL}[/math] is the loss reserve under the Chain Ladder method.

Calculate [math]f_2[/math] , the loss development factor from the paid-loss-development triangle at duration 2.

• 1.250
• 1.500
• 1.875
• 2.150
• 2.500

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: B

[[math]] \begin{aligned} &R_{BF} = (1- \frac{1}{F}) R_{LR} + \frac{1}{f}R_{CL} \\ & 400,000 = (1-\frac{1}{f})250,000 + \frac{1}{f} 437,500 \Rightarrow f = 1.25 = \prod_{j=3}^{\infty} f_j \\ &1,120, 000 = (1- \frac{1}{f})1,200,000 + \frac{1}{f} 1,050,000 \Rightarrow f = 1.875 = \prod_{j=2}^{\infty} f_j \\ &f_2 = \frac{1.875}{1.25} = 1.5. \end{aligned} [[/math]]

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.