Assignment 3 Solutions

Assignment 3 Solutions - 1 Solution Calculate ultimate AY...

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1. Solution Calculate ultimate AY and RY loss development factors: Cumulative LDFs Development Interval Accident Year Cumulative AY Report Year Cumulative RY 1-2 Years 1.500 2.382 1.100 1.210 2-3 Years 1.250 1.588 1.100 1.100 3-4 Years 1.100 1.271 1.000 1.000 4-5 Years 1.100 1.155 1.000 1.000 5-Ultimate 1.050 1.050 1.000 1.000 Calculate ultimate Accident Year and Report Year losses. AY/RY AY Incurred to Date AY LDF AY Ultimate RY Incurred to Date RY LDF RY Ultimate 2005 17,000 1.050 17,850 10,000 1.000 10,000 2006 21,000 1.155 24,255 16,000 1.000 16,000 2007 26,000 1.271 33,046 23,000 1.000 23,000 2008 25,000 1.588 39,700 28,000 1.100 30,800 2009 20,000 2.382 47,640 32,000 1.210 38,720 Total 109,000 162,491 109,000 118,520 Estimated unreported losses = AY Ultimate - RY Ultimate 43,971 2. Solution: i) Limited data ii) leveraging effect

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3. Solution Since loss development factors are for paid losses we can calculate unpaid losses directly: Accident Year Earned Premium Expected Ult Claim Ratio % Unpaid Unpaid 2005 1,000,000 0.65 0.0% - 2006 1,000,000 0.65 9.5% 61,765 2007 1,000,000 0.70 20.0% 140,000 2008 1,000,000 0.70 37.5% 262,500 2009 1,000,000 0.80 50.0% 400,000 Total 5,000,000 864,265 4. Solution a) Accident Year Earned Premium Incurred Loss Incurred LDF to Ultimate % Unreported Expected Loss Ratio B-F Method 2006 15,000 4,500 1.500 33.3% 65% 3,250 2007 16,000 4,800 1.750 42.9% 65% 4,457 2008 17,000 3,200 2.000 50.0% 65% 5,525 2009 18,000 2,500 4.500 77.8% 65% 9,100 Solution b) Accident Year Earned Premium Incurred Loss Incurred LDF to Ultimate % Unreported % Reported Used Up Premium Cape Cod LR Cape Cod IBNR 2006 15,000 4,500 1.500 33.3% 66.7% 10,000 45.0% 2,370 2007 16,000 4,800 1.750 42.9% 57.1% 9,143 52.5% 3,251 2008 17,000
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This note was uploaded on 02/08/2012 for the course ACTSC 463 taught by Professor Vankooten during the Fall '11 term at Waterloo.

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Assignment 3 Solutions - 1 Solution Calculate ultimate AY...

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