5. Reserves: Bornhuetter-Ferguson and Expected Loss Ratio.
The following information is available on earned premiums, expected loss ratios, and cumulative
payments made by the insurer:
Year of Occurrence
Earned Premium
Expected Loss Ratio
2015
15,000
0.60
2016
16,000
0.62
2017
17,000
0.65
2018
18,000
0.63
Year Oc
AD 0
AD 1
AD 2
AD 3
2015
6,500
8,100
9,000
9,000
2016
6,900
9,300
9,400
2017
7,400
9,500
2018
7,800
(You can use Excel or R, all calculations must be clear, explicit, and in order)
a) Calculate the accumulated reserve as of December 31, 2018, using the
Bornhuetter-Ferguson method with volume-weighted development factors.
Assume claims close after 2 years.
b) Calculate the accumulated reserve as of the same date, but under the
Expected Loss Ratio method (Loss Ratio).
