Review Exercises_2011

Review Exercises_2011 - 1. XYZ Insurance Company has been...

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1. XYZ Insurance Company has been writing business since 1/1/2005 and has provided you with following incurred loss data evaluated at 12/31/2009: Report Year Accident Year 2005 2006 2007 2008 2009 2005 10,000 4,000 2,000 1,000 - 2006 12,000 5,000 2,500 1,500 2007 16,000 6,500 3,500 2008 18,000 7,000 2009 20,000 Accident Year Report Year 1-2 Years 1.50 1.10 2-3 Years 1.25 1.10 3-4 Years 1.10 1.00 4-5 Years 1.10 1.00 5-Ultimate 1.05 1.00 Assuming the development factors are correct, estimate unreported losses as of 12/31/2009. 1. Solution Calculate ultimate AY and RY loss development factors: Cumulative LDFs Accident Year Report Year 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 LDF AY Ultimate 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 Development Interval Development Interval Cumulative AY Cumulative RY AY Incurred to Date RY Incurred to Date
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2. List two things that make the selection of a tail factor difficult. 2. Solution: i) Limited data ii) leveraging effect
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3. What is the estimate of unpaid claims as of 12/31/2009 for accident years 2005 to 2009, using the Bornhuetter-Ferguson technique and the following information? Earned Premium 2005 1,000,000 0.65 650,000 2006 1,000,000 0.65 650,000 2007 1,000,000 0.70 500,000 2008 1,000,000 0.70 500,000 2009 1,000,000 0.80 500,000 Accident Year Ultimate Paid Development Factors 2009 to Ultimate 2.000 2008 to Ultimate 1.600 2007 to Ultimate 1.250 2006 to Ultimate 1.105 2005 to Ultimate 1.000 3. Solution Since loss development factors are for paid losses we can calculate unpaid losses directly: Earned Premium % 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 Accident Year Expected Ult Claim Ratio Claims Paid to Date Accident Year Expected Ult Claim Ratio
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4. You are given the following information as at December 31, 2009: 2006 15,000 4,500 1.500 2007 16,000 4,800 1.750 2008 17,000 3,200 2.000 2009 18,000 2,500 4.500 The expected loss ratio for all accident years is 65%. The company has no exposure prior to 2006. a) Use the Bornhuetter-Ferguson method to calculate the IBNR for AY 2009 at December 31, 2009. b) Use the Cape Cod technique to calculate the IBNR for AY 2009 at December 31, 2009.
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Review Exercises_2011 - 1. XYZ Insurance Company has been...

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