UIUC FIN 431 - Loss Reserving (21 pages)

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Loss Reserving



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Finance 431 Property Liability Insurance Lecture 7 Loss Reserving Loss Reserving Anatomy of a claim 12 15 02 Auto accident 12 20 02 Insured reports accident to agent 1 7 03 Claim recorded 2 3 03 10 000 reserve set 1 8 04 Pay 3000 medical expenses offer settlement 15 000 reserve set 7 2 04 Offer refused 9 8 04 Lawsuit files 4 1 05 20 000 reserve 1 6 06 40 000 reserve 10 6 07 Court awards total 15 000 32 000 in Incurred loss development Accident Year 2002 2002 IBNR 2003 10 000 2004 18 000 2005 23 000 2006 43 000 2007 32 000 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 What is your answer to question 1 on Class Project 7 A B C D E 3 400 6 000 10 000 12 600 None of the above What is your answer to question 2 on Class Project 7 A B C D E 3 400 6 000 10 000 12 600 None of the above What is your answer to question 3 on Class Project 7 A B C D E 3 400 6 000 12 600 16 000 None of the above What is your answer to question 4 on Class Project 7 A B C D E 3 400 6 000 12 600 16 000 None of the above 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 Cumulative Loss Payments 000 omitted Accident Year 12 2000 5445 2001 5847 2002 5981 2003 7835 2004 9763 2005 10745 2006 14137 2007 15162 24 8602 9333 10835 12288 16280 16929 22253 Development Age Months 36 48 60 72 84 96 11052 12464 13064 13416 13847 14032 10699 11547 12592 13646 14015 12783 15337 17017 17506 16176 19511 21599 19843 23827 21478 Assume that no further losses are paid after 96 months Paid Loss Development Factors Accident Year 12 24 2000 1 580 2001 1 596 2002 1 812 2003 1 568 2004 1 668 2005 1 576 2006 1 574 Ave 1 625 Age 2 779 Ultimate Link Factors 24 36 36 48 1 285 1 128 1 146 1 079 1 180 1 200 1 316 1 206 1 219 1 201 1 269 48 60 1 048 1 090 1 110 1 107 60 72 72 84 84 96 1 027 1 032 1 013 1 084 1 027 1 029 1 236 1 163 1 089 1 047 1 030 1 013 1 710 1 384 1 190 1 092 1 043 1 013 How is 24 month ultimate paid loss development factor calculated on the prior exhibit A B C D E 1 384x1 190x1 043x1 013 1 625x1 236x1 163x1 089x1 047x1 030x1 013 1 236x1 163x1 089x1 047x1 030x1 013 1 384x1 236 None of the above Estimated Loss Reserves Based on Average Paid Loss Development Factors 000 omitted Age to Accident Paid to Ultimate Ultimate Year Date Factor Losses Reserve 2000 14032 1 000 14032 0 2001 14015 1 013 14197 182 2002 17506 1 043 18259 753 2003 21599 1 092 23586 1987 2004 23827 1 190 28354 4527 2005 21478 1 384 29726 8248 2006 22253 1 710 38053 15800 2007 15162 2 779 42135 26973 Total 149872 208342 58470 Loss Based on the prior exhibit what are the accident year 2005 losses evaluated as of 12 31 07 A B C D E 8 248 000 21 478 000 26 973 000 29 726 000 None of the above Expected Loss Ratio Method Estimated Ultimate Losses Expected Loss Ratio x Earned Premium Estimated Loss Reserve Estimated Ultimate Losses Losses Paid to Date Example 2007 Earned Premium 65 000 000 Expected Loss Ratio 60 Estimated Ultimate Losses 39 000 000 Losses Paid to Date 15 162 000 Estimated Loss Reserve 23 838 000 Bornhuetter Ferguson Method 2007 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 65 000 000 x 60 39 000 000 Estimated Loss Reserve 39 000 000 x 640 24 960 000 If you were applying the BornhuetterFerguson Method to accident year 2006 what would be the percent of losses expected to be paid after 12 31 07 A B C D E 1 1 1 236 191 1 1 1 574 365 1 1 1 71 415 1 1 2 779 640 None of the above Results of Different Loss Reserve Methods Accident Year 2007 Paid Loss Development Expected Loss Ratio Bornhuetter Ferguson 26 973 000 23 838 000 24 960 000 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 Incurred Loss Development Similar to paid loss development but includes case loss reserves Additional Reserving Requirements Loss Adjustment Expense Allocated Sometimes included with losses Unallocated Conclusion 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 estimate


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