You are given the following information on losses paid for each of AY1 through AY4:

The estimated loss reserve using the expected loss ratio method is 43,412.

Calculate X.

• 48,964
• 49,674
• 51,875
• 52,174
• 54,785

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

You are given:

• Accident Year	Cumulative Paid Losses through Development Year						Earned premium
  	0	1	2	3	4	5
  AY4	1,400	5,200	7,300	8,800	9,800	9,800	18,000
  AY5	2,200	6,400	8,800	10,200	11,500		20,000
  AY6	2,500	7,500	10,700	12,600			25,000
  AY7	2,800	8,700	12,900				26,000
  AY8	2,500	7,900					27,000
  AY9	2,600						28,000

• The expected loss ratio for each Accident Year is 0.550.

Calculate the total loss reserve using the Bornhuetter-Ferguson method and three-year arithmetic average paid loss development factors.

• 21,800
• 22,500
• 23,600
• 24,700
• 25,400

You are given:

1. An insurance company was formed to write workers compensation business in CY1.
2. Earned premium in CY1 was 1,000,000.
3. Earned premium growth through CY3 has been constant at 20% per year (compounded).
4. The expected loss ratio for AY1 is 60%.
5. As of December 31, CY3, the company’s reserving actuary believes the expected loss ratio has increased two percentage points each accident year since the company’s inception.
6. Selected incurred loss development factors are as follows:

Calculate the total IBNR reserve as of December 31, CY3 using the Bornhuetter-Ferguson method.

• 964,000
• 966,000
• 968,000
• 970,000
• 972,000

You are given the following information:

1. Case reserves = 187,047
2. Losses paid-to-date = 243,005
3. Age-to-ultimate incurred loss development factor = 1.08
4. IBNR using Bornhuetter-Ferguson method = 47,387

Calculate the absolute difference in the IBNR based on the chain-ladder method and the expected loss ratio method.

• 12,983
• 43,787
• 98,101
• 146,754
• 175,268

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:

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