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622 ESTIMATING THE WORKERS COMPENSATION TAILTABLE 5.7Trends in Five-Year Paid Loss Development FactorsDevelopment YearsAY 10/5 15/10 20/15 25/20 30/25 35/30 40/35 45/40 50/45 55/50 60/55 65/60 70/65 75/70 80/75 85/801970 1.182 1.082 1.091 1.103 1.113 1.114 1.107 1.097 1.084 1.069 1.053 1.037 1.022 1.010 1.004 1.0011975 1.183 1.083 1.092 1.105 1.115 1.116 1.110 1.099 1.086 1.071 1.055 1.039 1.023 1.011 1.004 1.0011980 1.184 1.084 1.094 1.107 1.118 1.119 1.114 1.103 1.089 1.073 1.057 1.040 1.024 1.012 1.004 1.0011985 1.185 1.084 1.095 1.109 1.120 1.123 1.117 1.106 1.092 1.076 1.059 1.042 1.026 1.013 1.005 1.0021990 1.186 1.085 1.096 1.111 1.123 1.126 1.120 1.109 1.094 1.078 1.061 1.044 1.027 1.014 1.005 1.0021995 1.186 1.086 1.097 1.113 1.126 1.129 1.123 1.112 1.097 1.081 1.063 1.046 1.029 1.015 1.006 1.0022000 1.187 1.087 1.098 1.114 1.128 1.132 1.126 1.115 1.100 1.083 1.065 1.048 1.030 1.015 1.006 1.002TABLE 5.8PLDFs Factors Indicated by the Trended MortalityModel During Early Years of DevelopmentYears of DevelopmentAY 2 3 4 5 6 7 8 9 10 11 121990 6.81875 1.59471 1.16775 1.09383 1.05240 1.04154 1.03101 1.02670 1.02182 1.01604 1.016181991 6.81875 1.59488 1.16781 1.09387 1.05243 1.04157 1.03104 1.02673 1.02185 1.01607 1.016211992 6.81875 1.59505 1.16786 1.09392 1.05246 1.04160 1.03107 1.02676 1.02187 1.01609 1.016231993 6.81875 1.59522 1.16792 1.09396 1.05250 1.04163 1.03110 1.02679 1.02190 1.01611 1.016251994 6.81875 1.59539 1.16797 1.09400 1.05253 1.04166 1.03113 1.02681 1.02192 1.01613 1.016281995 6.81875 1.59557 1.16803 1.09405 1.05256 1.04169 1.03115 1.02684 1.02195 1.01615 1.016301996 6.81875 1.59571 1.16807 1.09408 1.05259 1.04172 1.03118 1.02686 1.02197 1.01617 1.016321997 6.81875 1.59586 1.16812 1.09412 1.05261 1.04174 1.03120 1.02688 1.02199 1.01618 1.016341998 6.81875 1.59601 1.16816 1.09415 1.05263 1.04176 1.03122 1.02691 1.02201 1.01620 1.016361999 6.81875 1.59616 1.16821 1.09419 1.05266 1.04179 1.03124 1.02693 1.02203 1.01622 1.016382000 6.81875 1.59631 1.16825 1.09422 1.05268 1.04181 1.03126 1.02695 1.02205 1.01623 1.016392001 6.81875 1.59647 1.16830 1.09426 1.05271 1.04184 1.03129 1.02697 1.02208 1.01625 1.016422002 6.81875 1.59662 1.16835 1.09430 1.05273 1.04186 1.03131 1.02699 1.02210 1.01627 1.01644is small. It is small enough that it would not be detectable to anexperienced actuary reviewing historical PLDFs. This becomeseven more evident if we look at different sections of the typicaltriangle of paid loss development factors that are generated bythe trended mortality model.In Table 5.8 the individual PLDFs generated by the modelare displayed for AYs 1990—2002 for the earliest developmentyears.
ESTIMATING THE WORKERS COMPENSATION TAIL 623TABLE 5.9PLDFs Indicated by the Trended Mortality ModelDuring Later Years of DevelopmentYear of DevelopmentAY 27 28 29 30 31 32 33 34 35 36 371966 1.02103 1.02124 1.02139 1.02147 1.02149 1.02146 1.02136 1.02121 1.02101 1.02077 1.020491967 1.02112 1.02134 1.02149 1.02157 1.02160 1.02156 1.02147 1.02132 1.02113 1.02088 1.020601968 1.02121 1.02143 1.02159 1.02168 1.02170 1.02167 1.02158 1.02143 1.02124 1.02100 1.020721969 1.02130 1.02153 1.02168 1.02178 1.02181 1.02178 1.02169 1.02154 1.02135 1.02111 1.020831970 1.02140 1.02163 1.02179 1.02189 1.02192 1.02189 1.02180 1.02166 1.02147 1.02123 1.020951971 1.02148 1.02171 1.02187 1.02198 1.02201 1.02199 1.02190 1.02176 1.02157 1.02133 1.021061972 1.02155 1.02179 1.02196 1.02207 1.02211 1.02209 1.02200 1.02187 1.02168 1.02144 1.021161973 1.02163 1.02187 1.02205 1.02216 1.02220 1.02218 1.02211 1.02197 1.02178 1.02155 1.021271974 1.02170 1.02195 1.02213 1.02225 1.02230 1.02228 1.02221 1.02208 1.02189 1.02165 1.021381975 1.02178 1.02203 1.02222 1.02234 1.02239 1.02238 1.02231 1.02218 1.02200 1.02176 1.021481976 1.02188 1.02214 1.02233 1.02245 1.02250 1.02250 1.02243 1.02230 1.02211 1.02188 1.021601977 1.02199 1.02225 1.02244 1.02256 1.02262 1.02261 1.02254 1.02241 1.02223 1.02200 1.02172The constant PLDFs in the column for DY 2 merely reflect asimplifying assumption in the model.In Table 5.9 individual PLDFs generated by the model aredisplayed for accident years 1966—1977 for the most mature historicaldevelopment years. Projected PLDFs for the short-termfuture are also shown below the diagonal.Table 5.10 provides an example of the kinds of errors in estimatingfuture incremental payments that can occur when it isassumed that PLDFs for each year of development hold constant.First, a PLDF of 1.02138 is selected as the average of the latestfour historical factors during the 34th year of development (theboxed items in Table 5.9). By comparing this selection with thetrue underlying trended PLDF, the percentage error in incrementalpayments for that development year is shown for every fifthAY. These errors assume, however, that other similar errors didnot occur during preceding development years.Though all of the errors above are small, these errors compoundsignificantly in the calculation of tail factors, which arethe product of numerous individual PLDFs.
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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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Editorial Committee, Proceedings Ed
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RISKINESS LEVERAGE MODELS 81EXHIBIT
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ADDRESS TO NEW MEMBERS 151ateship a
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Volume XCII, Part 2 No. 177PROCEEDI
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WHEN CAN ACCIDENT YEARS BE REGARDED
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ARCHITECTURE FOR RESIDENTIAL PROPER
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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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