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UIUC FIN 431 - Loss Reserving

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Finance 431: Property-Liability Insurance Lecture 7: Loss ReservingLoss ReservingDefinitionsWhat is your answer to question 1 on Class Project #7?What is your answer to question 2 on Class Project #7?What is your answer to question 3 on Class Project #7?What is your answer to question 4 on Class Project #7?Loss reserve methodsCumulative Loss Payments (000 omitted)Paid Loss Development FactorsHow is 24 month-ultimate paid loss development factor calculated on the prior exhibit?Estimated Loss Reserves Based on Average Paid Loss Development Factors (000 omitted)Based on the prior exhibit, what are the accident year 2005 losses evaluated as of 12/31/07?Expected Loss Ratio MethodBornhuetter-Ferguson Method 2007 Accident YearIf you were applying the Bornhuetter-Ferguson Method to accident year 2006, what would be the percent of losses expected to be paid after 12/31/07?Results of Different Loss Reserve Methods – Accident Year 2007Frequency and Severity EstimatesIncurred Loss DevelopmentAdditional Reserving RequirementsConclusionFinance 431:Property-Liability InsuranceLecture 7:Loss ReservingLoss ReservingAnatomy of a claim12/15/02 Auto accident12/20/02 Insured reports accident to agent1/7/03 Claim recorded2/3/03 $10,000 reserve set1/8/04 Pay $3000 medical expenses; offer $15,000 settlement; $15,000 reserve set7/2/04 Offer refused9/8/04 Lawsuit files4/1/05 $20,000 reserve1/6/06 $40,000 reserve10/6/07 Court awards $32,000 in totalIncurred loss developmentAccident Year 20022002 IBNR2003 $10,0002004 $18,0002005 $23,0002006 $43,0002007 $32,000DefinitionsIndividual claim file estimatesPaid loss developmentConsiders only loss paymentsPaid loss development factorsIncurred loss developmentPaid plus case reservesIncurred loss development factorsLoss adjustment expensesAllocatedUnallocatedWhat is your answer to question 1 on Class Project #7?A) -$3,400B) $6,000C) $10,000D) $12,600E) None of the aboveWhat is your answer to question 2 on Class Project #7?A) -$3,400B) $6,000C) $10,000D) $12,600E) None of the aboveWhat is your answer to question 3 on Class Project #7?A) -$3,400B) $6,000C) $12,600D) $16,000E) None of the aboveWhat is your answer to question 4 on Class Project #7?A) -$3,400B) $6,000C) $12,600D) $16,000E) None of the aboveLoss reserve methodsUnsophisticated methods:Case reserve plusExpected loss ratio methodMore accurate methods:Chain ladder or loss development triangle methodBornhuetter-Ferguson methodFrequency and severity estimatesCumulative Loss Payments(000 omitted)Accident Development Age (Months)Year 12 24 36 48 60 72 84 962000 5445 8602 11052 12464 13064 13416 13847 140322001 5847 9333 10699 11547 12592 13646 140152002 5981 10835 12783 15337 17017 175062003 7835 12288 16176 19511 215992004 9763 16280 19843 238272005 10745 16929 214782006 14137 222532007 15162Assume that no further losses are paid after 96 months.Paid Loss Development FactorsAccident Link FactorsYear 12-24 24-36 36-48 48-60 60-72 72-84 84-96 2000 1.580 1.285 1.128 1.048 1.027 1.032 1.013 2001 1.596 1.146 1.079 1.090 1.084 1.0272002 1.812 1.180 1.200 1.110 1.0292003 1.568 1.316 1.206 1.1072004 1.668 1.219 1.2012005 1.576 1.2692006 1.574Ave. 1.625 1.236 1.163 1.089 1.047 1.030 1.013Age- 2.779 1.710 1.384 1.190 1.092 1.043 1.013UltimateHow is 24 month-ultimate paid loss development factor calculated on the prior exhibit?A) 1.384x1.190x1.043x1.013B) 1.625x1.236x1.163x1.089x1.047x1.030x1.013C) 1.236x1.163x1.089x1.047x1.030x1.013D) 1.384x1.236E) None of the aboveEstimated Loss Reserves Based on Average Paid Loss Development Factors(000 omitted)Age toAccident Paid to Ultimate Ultimate LossYear Date Factor Losses Reserve2000 14032 1.000 14032 02001 14015 1.013 14197 1822002 17506 1.043 18259 7532003 21599 1.092 23586 19872004 23827 1.190 28354 45272005 21478 1.384 29726 82482006 22253 1.710 38053 158002007 15162 2.779 42135 26973Total 149872 208342 58470Based on the prior exhibit, what are the accident year 2005 losses evaluated as of 12/31/07?A) $8,248,000B) $21,478,000 C) $26,973,000D) $29,726,000E) None of the aboveExpected Loss Ratio MethodEstimated Ultimate Losses = Expected Loss Ratio x Earned PremiumEstimated Loss Reserve = Estimated Ultimate Losses - Losses Paid to DateExample2007 Earned Premium = 65,000,000Expected Loss Ratio = 60%Estimated Ultimate Losses = 39,000,000Losses Paid to Date = 15,162,000Estimated Loss Reserve 23,838,000Bornhuetter-Ferguson Method2007 Accident YearEstimated Loss Reserve = Total Expected Losses x % of Losses to Be Paid in Future% of Losses to Be Paid in Future = 1-(1/Age-Ultimate Factor)Example: 12 Month-Ultimate = 2.779% of Losses Paid After 12 Months = 1-1/2.779=.640Total Expected Losses = 65,000,000 x .60=39,000,000Estimated Loss Reserve = 39,000,000 x .640 = 24,960,000If you were applying the Bornhuetter-Ferguson Method to accident year 2006, what would be the percent of losses expected to be paid after 12/31/07?A) 1-1/1.236 = .191B) 1-1/1.574 = .365C) 1-1/1.71 = .415D) 1-1/2.779 = .640E) None of the aboveResults of Different Loss Reserve Methods – Accident Year 2007Paid Loss Development 26,973,000Expected Loss Ratio 23,838,000Bornhuetter-Ferguson 24,960,000Frequency and Severity EstimatesCalculate Incurred Claim Counts Determine Loss Frequency = # Claims/ExposureDetermine Average Payment per Claim or Average Incurred Loss per Claim (Severity)Trend Frequency and Severity SeparatelyCombine to Determine Ultimate Incurred LossesIncurred Loss DevelopmentSimilar to paid loss development, but includes case loss reservesAdditional Reserving RequirementsLoss Adjustment ExpenseAllocatedSometimes included with lossesUnallocatedConclusion•Loss reserving combines calculations with actuarial judgement•To set accurate loss reserves requires thorough knowledge of claim settlement practices, especially regarding any changes•Current loss reserving approaches involves estimating loss reserve ranges, rather than setting a point


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