Functions to Reproduce Clark's Tables
Table65.rdPrint the tables on pages 64, 65, and 68 of Clark's paper.
Details
These exhibits give some of the details behind the calculations producing the estimates of future values (a.k.a. "Reserves" in Clark's paper). Table65 works for both the "LDF" and the "CapeCod" methods. Table64 is specific to "LDF", Table68 to "CapeCod".
References
Clark, David R., "LDF Curve-Fitting and Stochastic Reserving: A Maximum Likelihood Approach", Casualty Actuarial Society Forum, Fall, 2003 https://www.casact.org/sites/default/files/database/forum_03fforum_03ff041.pdf
Examples
Table65(ClarkLDF(GenIns, maxage=20))
#> Origin CurrentValue FutureValue ProcessSE ProcessCV ParameterSE ParameterCV
#> 1 1 3901463 666530.8 209582.5 31.4 156593.2 23.5
#> 2 2 5339085 1157423.1 275610.3 23.8 254781.7 22.0
#> 3 3 4909315 1365086.0 298810.1 21.9 295848.6 21.7
#> 4 4 4588268 1665693.7 329605.5 19.8 353535.0 21.2
#> 5 5 3873311 1886481.4 350361.0 18.6 397791.3 21.1
#> 6 6 3691712 2514880.3 404131.2 16.1 513654.8 20.4
#> 7 7 3483130 3546784.7 479542.3 13.5 698509.6 19.7
#> 8 8 2864498 4896501.4 563084.2 11.5 961057.8 19.6
#> 9 9 1363294 4991635.1 568138.4 11.4 1218732.2 24.4
#> 10 10 344014 6223706.3 634046.3 10.2 2821745.5 45.3
#> Total 34358090 28914722.7 1369565.1 4.7 4651504.5 16.1
#> StdError TotalCV
#> 1 261622.3 39.3
#> 2 375332.8 32.4
#> 3 420492.4 30.8
#> 4 483349.5 29.0
#> 5 530085.6 28.1
#> 6 653577.3 26.0
#> 7 847275.9 23.9
#> 8 1113865.3 22.7
#> 9 1344652.2 26.9
#> 10 2892103.5 46.5
#> 4848938.3 16.8
Table64(ClarkLDF(GenIns, maxage=20))
#> Origin CurrentValue CurrentAge AgeUsed GrowthFunction Ldf TruncatedLdf
#> 1 NA 20 19.5 0.90550697 1.104354 1.000000
#> 2 1 3901463 10 9.5 0.77338151 1.293023 1.170841
#> 3 2 5339085 9 8.5 0.74418113 1.343759 1.216783
#> 4 3 4909315 8 7.5 0.70850094 1.411431 1.278060
#> 5 4 4588268 7 6.5 0.66433229 1.505271 1.363033
#> 6 5 3873311 6 5.5 0.60892995 1.642225 1.487046
#> 7 6 3691712 5 4.5 0.53860005 1.856665 1.681223
#> 8 7 3483130 4 3.5 0.44865388 2.228890 2.018275
#> 9 8 2864498 3 2.5 0.33421249 2.992108 2.709375
#> 10 9 1363294 2 1.5 0.19425429 5.147891 4.661452
#> 11 10 344014 1 0.5 0.04743002 21.083696 19.091433
#> 12 Total 34358090 NA NA NA NA NA
#> LossesAtMaxage FutureValue
#> 1 NA NA
#> 2 4567994 666530.8
#> 3 6496508 1157423.1
#> 4 6274401 1365086.0
#> 5 6253962 1665693.7
#> 6 5759792 1886481.4
#> 7 6206592 2514880.3
#> 8 7029915 3546784.7
#> 9 7760999 4896501.4
#> 10 6354929 4991635.1
#> 11 6567720 6223706.3
#> 12 63272813 28914722.7
X <- GenIns
colnames(X) <- 12*as.numeric(colnames(X))
Table65(ClarkCapeCod(X, Premium=10000000+400000*0:9, maxage=Inf))
#> Origin CurrentValue FutureValue ProcessSE ProcessCV ParameterSE ParameterCV
#> 1 1 3901463 1323698 284493.9 21.5 340851.2 25.7
#> 2 2 5339085 1556996 308547.7 19.8 380563.1 24.4
#> 3 3 4909315 1846297 335992.3 18.2 424217.1 23.0
#> 4 4 4588268 2209996 367598.9 16.6 471286.9 21.3
#> 5 5 3873311 2673721 404330.5 15.1 520246.7 19.5
#> 6 6 3691712 3272829 447342.5 13.7 567800.6 17.3
#> 7 7 3483130 4053931 497870.8 12.3 607956.3 15.0
#> 8 8 2864498 5069599 556756.5 11.0 632156.8 12.5
#> 9 9 1363294 6344850 622858.1 9.8 635453.9 10.0
#> 10 10 344014 7738201 687857.5 8.9 642428.6 8.3
#> Total 34358090 36090118 1485499.9 4.1 5169409.8 14.3
#> StdError TotalCV
#> 1 443977.8 33.5
#> 2 489928.5 31.5
#> 3 541157.1 29.3
#> 4 597695.8 27.0
#> 5 658892.9 24.6
#> 6 722850.5 22.1
#> 7 785802.9 19.4
#> 8 842377.6 16.6
#> 9 889805.5 14.0
#> 10 941202.7 12.2
#> 5378615.7 14.9
Table68(ClarkCapeCod(X, Premium=10000000+400000*0:9, maxage=Inf))
#> Origin Premium CurrentAge AgeUsed GrowthFunction FutureGrowthFactor
#> 1 NA Inf Inf 1.00000000 0.0000000
#> 2 1 1.00e+07 120 114 0.77828466 0.2217153
#> 3 2 1.04e+07 108 102 0.74923842 0.2507616
#> 4 3 1.08e+07 96 90 0.71365834 0.2863417
#> 5 4 1.12e+07 84 78 0.66949336 0.3305066
#> 6 5 1.16e+07 72 66 0.61393113 0.3860689
#> 7 6 1.20e+07 60 54 0.54317615 0.4568238
#> 8 7 1.24e+07 48 42 0.45240260 0.5475974
#> 9 8 1.28e+07 36 30 0.33660779 0.6633922
#> 10 9 1.32e+07 24 18 0.19489202 0.8051080
#> 11 10 1.36e+07 12 6 0.04696731 0.9530327
#> 12 Total 1.18e+08 NA NA NA NA
#> PremiumxELR FutureValue
#> 1 NA NA
#> 2 5970260 1323698
#> 3 6209071 1556996
#> 4 6447881 1846297
#> 5 6686692 2209996
#> 6 6925502 2673721
#> 7 7164313 3272829
#> 8 7403123 4053931
#> 9 7641933 5069599
#> 10 7880744 6344850
#> 11 8119554 7738201
#> 12 70449074 36090118