PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

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638 ESTIMATING THE WORKERS COMPENSATION TAILTABLE 8.2Comparison of Different Types of MPD ReserveEstimatesAssuming SSA 2000 Male & Female Mortality Tables and 9% Medical Cost Escalation(A) (B) (C) (D) (E)Reserve ($000s) at Eval. DateRatio of Ratio ofFirst Second Third Second ThirdMethod Method Method Method Method(Zero (9% (Total Reserve ReserveAge at Inflation Inflation Expected to First to SecondReserve Case Case Future Method MethodDate Reserve) Reserve) Payout) Reserve ReserveMale Claimants20 $273.7 $7,333.9 $11,318.1 26.795 1.54330 227.3 2,989.5 4,816.3 13.155 1.61140 181.2 1,321.0 2,042.3 7.290 1.54650 137.3 590.0 864.0 4.298 1.46460 96.7 265.3 362.9 2.744 1.36870 62.9 123.5 153.2 1.965 1.24080 36.0 57.1 63.4 1.587 1.110Female Claimants20 $301.0 $10,796.0 $16,724.2 35.867 1.54930 252.4 4,641.7 7,069.1 18.390 1.52340 204.7 2,005.7 2,983.6 9.800 1.48850 158.4 873.8 1,254.5 5.516 1.43660 115.1 384.3 524.0 3.341 1.36370 77.0 165.0 217.3 2.144 1.31780 45.2 76.3 87.2 1.690 1.142do not increase with the age of the claimant. This was done tosimplify the presentation of methods that are already complex. Ifthe tendency of incremental medical severities to increase withage were incorporated into these methods, the differences betweenthe reserves projected by these methods would expandnoticeably.
ESTIMATING THE WORKERS COMPENSATION TAIL 6399. ESTIMATING THE VARIABILITY OF THE MPD RESERVE WITH AMARKOV CHAIN SIMULATIONThe size of loss distribution for the medical component of asingle PD claim is far more skewed to the right than can be modeledby distributions commonly used by casualty actuaries. Thisdistribution can be described by the ultimate costs in Column (F)of Tables 8.1A and 8.1B, with the associated confidence levelstakenfromColumn(D).Inattemptingtofindadistributionthatproduced a reasonable fit, it was necessary to first transform theultimate cost amounts by taking the natural log of the natural logof the natural log and then taking the nth root before a commondistribution could be found. Taking the fifth root of the triplenatural log appears to produce a distribution of ultimate coststhat conforms well with an extreme value distribution. The factthat such intense transformations were needed suggests that a totallydifferent approach than fitting commonly used distributionsshould be used.As is indicated from Table 8.2, the ratio of the expected valueof the individual case reserve to the projected payments throughexpected year of death estimate varies dramatically according tothe gender and current age of each claimant. This suggests thatthe variability of the total MPD reserve can best be modeledby simulating the variability of the future payout for each claimseparately. Table 9.1 provides a sample framework for this typeof simulation. The sample insurer has 10 open PD claims.An individual row in Table 9.1 is devoted to each open claim.Census data on the gender and current age of each living PDclaimants appears in two columns on the left side of the table.Consider claim number 1 in the top row. Actual medical paymentsin 2003 were $3,000. A random number between 0 and 1is generated. If that number is between 0 and q 75 , the claimantdies during 2004. Recall that q x denotes the probability of deathat age x, given survival to that age. If the random number isgreater than q 75 , the claimant lives throughout 2004.
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VOLUME XCII NUMBERS 176 and 177PROC
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FOREWORDActuarial science originate
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2005 PROCEEDINGSCONTENTS OF VOLUME
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2005 PROCEEDINGSCONTENTS OF VOLUME
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Editorial Committee, Proceedings Ed
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AN EXAMINATION OF THE INFLUENCE OF
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RISKINESS LEVERAGE MODELSRODNEY KRE
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RISKINESS LEVERAGE MODELS 59APPENDI
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DISCUSSION OF A PAPER PRESENTED AT
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RISKINESS LEVERAGE MODELS 63known t
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RISKINESS LEVERAGE MODELS 65to be a
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RISKINESS LEVERAGE MODELS 79REFEREN
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RISKINESS LEVERAGE MODELS 81EXHIBIT
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ADDRESS TO NEW MEMBERS 151ateship a
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ADDRESS TO NEW MEMBERS 153You shoul
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ADDRESS TO NEW MEMBERS 155strength
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MINUTES OF THE 2005 CAS SPRING MEET
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MINUTES OF THE 2005 SPRING MEETING
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Volume XCII, Part 2 No. 177PROCEEDI
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MODELING FINANCIAL SCENARIOS 179Bab
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WHEN CAN ACCIDENT YEARS BE REGARDED
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ARCHITECTURE FOR RESIDENTIAL PROPER
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DISCUSSION OF PAPER PUBLISHED INVOL
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THE “MODIFIED BORNHUETTER-FERGUSO
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ADDRESS TO NEW MEMBERS-NOVEMBER 14,
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ADDRESS TO NEW MEMBERS 743Now to an
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MINUTES OF THE 2005 CAS ANNUAL MEET
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REPORT OF THE VICE PRESIDENT-ADMINI
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2005 EXAMINATIONS—SUCCESSFUL CAND
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OBITUARIESROBERT GRANT ESPIECLYDE H
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OBITUARIES 825SIDNEY M. HAMMER1931
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OBITUARIES 827J. GARY LaROSE1947—
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OBITUARIES 829PAUL J. SCHEEL SR.193
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OBITUARIES 831LEO M. STANKUSCirca 1
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INDEX TO VOLUME XCIIPage2005 EXAMIN
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835GRAVES, CLYDE H.INDEX—CONTINUE
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837INDEX—CONTINUEDREPORT OF THE V
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PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

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