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Loss Reserving Anatomy of a claim 12/15/99 Auto accident 12/20/99 Insured reports accident to agent 1/7/00 Claim recorded 2/3/00 $10,000 reserve set 1/8/01.

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Presentation on theme: "Loss Reserving Anatomy of a claim 12/15/99 Auto accident 12/20/99 Insured reports accident to agent 1/7/00 Claim recorded 2/3/00 $10,000 reserve set 1/8/01."— Presentation transcript:

1 Loss Reserving Anatomy of a claim 12/15/99 Auto accident 12/20/99 Insured reports accident to agent 1/7/00 Claim recorded 2/3/00 $10,000 reserve set 1/8/01 Pay $3000 medical expenses; offer $15,000 settlement; $15,000 reserve set 7/2/01 Offer refused 9/8/01 Lawsuit files 4/1/02 $20,000 reserve 1/6/03 $40,000 reserve 10/6/04 Court awards $32,000 Incurred loss development Accident Year 1999 1999 IBNR 2000$10,000 2001$18,000 2002$23,000 2003 $43,000 2004$32,000

2 Definitions Individual claim file estimates Paid loss development Considers only loss payments Paid loss development factors Incurred loss development Paid plus case reserves Incurred loss development factors Loss adjustment expenses Allocated Unallocated

3 Loss reserve methods Unsophisticated methods: Case reserve plus Expected loss ratio method More accurate methods: Chain ladder or loss development triangle method Bornhuetter-Ferguson method Frequency and severity estimates

4 Cumulative Loss Payments Accident Development Age (Months) Year 12 24 36 48 60 72 84 96 1997 5445 8602110521246413064134161384714032 1998 5847 93331069911547125921364614015 1999 59811083512783153371701717506 2000 783512288161761951121599 2001 9763162801984323827 2002107451692921478 20031413722253 200415162 Assume that no further losses are paid after 96 months.

5 Paid Loss Development Factors Accident Link Factors Year 12-2424-3636-4848-6060-7272-8484-96 19971.5801.2851.1281.0481.0271.0321.013 19981.5961.1461.0791.0901.0841.027 19991.8121.1801.2001.1101.029 20001.5681.3161.2061.107 20011.6681.2191.201 20021.5761.269 20031.574 Ave.1.6251.2361.1631.0891.0471.0301.013 Age-2.7791.7101.3841.1901.0921.0431.013 Ultimate

6 Estimated Loss Reserves Based on Average Paid Loss Development Factors Age to Accident Paid to UltimateUltimateLoss Year DateFactorLossesReserve 1997 140321.00014032 0 1998 140151.01314197 182 1999 175061.04318259 753 2000 215991.09223586 1987 2001 238271.19028354 4527 2002214781.38429726 8248 2003222531.71038053 15800 2004151622.77942135 26973 Total 149872 208342 58470

7 Expected Loss Ratio Method Estimated Ultimate Losses = Expected Loss Ratio x Earned Premium Estimated Loss Reserve = Estimated Ultimate Losses - Losses Paid to Date Example 2004 Earned Premium = 65,000 Expected Loss Ratio = 60% Estimated Ultimate Losses = 39,000 Losses Paid to Date = 15,162 Estimated Loss Reserve23,838

8 Bornhuetter-Ferguson Method 2004 Accident Year Estimated 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=.640 Total Expected Losses = 65,000 x.60=39,000 Estimated Loss Reserve = 39,000 x.640 = 24,960

9 Results of Different Loss Reserve Methods – Accident Year 2004 Paid Loss Development26,973 Expected Loss Ratio23,838 Bornhuetter-Ferguson24,960

10 Frequency and Severity Estimates Calculate Incurred Claim Counts Determine Loss Frequency = # Claims/Exposure Determine Average Payment per Claim or Average Incurred Loss per Claim (Severity) Trend Frequency and Severity Separately Combine to Determine Ultimate Incurred Losses

11 Incurred Loss Development Similar to paid loss development, but includes case loss reserves

12 Additional Reserving Requirements Loss Adjustment Expense Allocated Sometimes included with losses Unallocated


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