Class "MultiChainLadder" of Multivariate Chain-Ladder Results
MultiChainLadder-class.RdThis class includes the first and second moment estimation result using the multivariate reserving methods in chain-ladder. Several primitive methods and statistical methods are also created to facilitate further analysis.
Objects from the Class
Objects can be created by calls of the form new("MultiChainLadder", ...), or they could also be a result of calls from MultiChainLadder or JoinFitMse.
Slots
model:Object of class
"character". Either "MCL" or "GMCL".Triangles:Object of class
"triangles". Input triangles.models:Object of class
"list". Fitted regression models usingsystemfit.coefficients:Object of class
"list". Estimated regression coefficients.coefCov:Object of class
"list". Estimated variance-covariance matrix of coefficients.residCov:Object of class
"list". Estimated residual covariance matrix.fit.method:Object of class
"character". Could be values of "SUR" or "OLS".delta:Object of class
"numeric". Parameter for weights.int:Object of class
"NullNum". Indicator of which periods have intercepts.mse.ay:Object of class
"matrix". Conditional mse for each accident year.mse.ay.est:Object of class
"matrix". Conditional estimation mse for each accident year.mse.ay.proc:Object of class
"matrix". Conditional process mse for each accident year.mse.total:Object of class
"matrix". Conditional mse for aggregated accident years.mse.total.est:Object of class
"matrix". Conditional estimation mse for aggregated accident years.mse.total.proc:Object of class
"matrix". Conditional process mse for aggregated accident years.FullTriangles:Object of class
"triangles". Completed triangles.restrict.regMat:Object of class
"NullList"
Extends
Class "MultiChainLadderFit", directly.
Class "MultiChainLadderMse", directly.
Methods
- $
signature(x = "MultiChainLadder"): Method for primitive function"$". It extracts a slot ofxwith a specified slot name, just as in list.- [[
signature(x = "MultiChainLadder", i = "numeric", j = "missing"): Method for primitive function"[[". It extracts the i-th slot of a"MultiChainLadder"object, just as in list.icould be a vector.- [[
signature(x = "MultiChainLadder", i = "character", j = "missing"): Method for primitive function"[[". It extracts the slots of a"MultiChainLadder"object with names ini, just as in list.icould be a vector.- coef
signature(object = "MultiChainLadder"): Method for functioncoef, to extract the estimated development matrix. The output is a list.- fitted
signature(object = "MultiChainLadder"): Method for functionfitted, to calculate the fitted values in the original triangles. Note that the return value is a list of fitted valued based on the original scale, not the model scale which is first divided by \(Y_{i,k}^{\delta/2}\).- names
signature(x = "MultiChainLadder"): Method for functionnames, which returns the slot names of a"MultiChainLadder"object.- plot
signature(x = "MultiChainLadder", y = "missing"): Seeplot,MultiChainLadder,missing-method.- residCov
signature(object = "MultiChainLadder"): S4 generic function and method to extract residual covariance from a"MultiChainLadder"object.- residCor
signature(object = "MultiChainLadder"): S4 generic function and method to extract residual correlation from a"MultiChainLadder"object.- residuals
signature(object = "MultiChainLadder"): Method for functionresiduals, to extract residuals from a system of regression equations. These residuals are based on model scale, and will not be equivalent to those on the original scale if \(\delta\) is not set to be 0. One should userstandardinstead, which is independent of the scale.- resid
signature(object = "MultiChainLadder"): Same asresiduals.- rstandard
signature(model = "MultiChainLadder"): S4 generic function and method to extract standardized residuals from a"MultiChainLadder"object.- show
signature(object = "MultiChainLadder"): Method forshow.- summary
signature(object = "MultiChainLadder"): Seesummary,MultiChainLadder-method.- vcov
signature(object = "MultiChainLadder"): Method for functionvcov, to extract the variance-covariance matrix of a"MultiChainLadder"object. Note that the result is a list ofBcov, that is the variance-covariance matrix of the vectorized \(B\).
Author
Wayne Zhang actuary_zhang@hotmail.com
Examples
# example for class "MultiChainLadder"
data(liab)
fit.liab <- MultiChainLadder(Triangles = liab)
fit.liab
#> $`Summary Statistics for Triangle 1`
#> Latest Dev.To.Date Ultimate IBNR S.E CV
#> 1 549,589 1.0000 549,589 0 0 0.0000
#> 2 562,795 0.9966 564,740 1,945 1,743 0.8961
#> 3 602,710 0.9913 608,013 5,303 6,720 1.2673
#> 4 784,632 0.9868 795,128 10,496 8,154 0.7769
#> 5 768,373 0.9805 783,649 15,276 10,497 0.6871
#> 6 811,100 0.9688 837,214 26,114 16,269 0.6230
#> 7 896,728 0.9544 939,595 42,867 19,154 0.4468
#> 8 1,022,241 0.9301 1,099,087 76,846 22,726 0.2957
#> 9 1,019,303 0.8818 1,155,890 136,587 29,055 0.2127
#> 10 1,141,750 0.7970 1,432,561 290,811 36,849 0.1267
#> 11 1,174,196 0.6761 1,736,765 562,569 57,024 0.1014
#> 12 1,032,684 0.4999 2,065,835 1,033,151 88,941 0.0861
#> 13 772,971 0.2907 2,658,834 1,885,863 192,733 0.1022
#> 14 204,325 0.0901 2,268,006 2,063,681 282,477 0.1369
#> Total 11,343,397 0.6484 17,494,907 6,151,510 419,293 0.0682
#>
#> $`Summary Statistics for Triangle 2`
#> Latest Dev.To.Date Ultimate IBNR S.E CV
#> 1 391,428 1.000 391,428 0 0 0.0000
#> 2 483,974 1.000 483,839 -135 604 -4.4846
#> 3 540,742 1.001 540,020 -722 1,324 -1.8323
#> 4 485,016 0.998 486,242 1,226 2,868 2.3394
#> 5 507,752 0.998 508,744 992 3,158 3.1844
#> 6 549,693 0.994 552,877 3,184 5,388 1.6923
#> 7 635,452 0.994 639,272 3,820 6,187 1.6193
#> 8 648,365 0.985 658,591 10,226 7,454 0.7289
#> 9 663,152 0.968 684,957 21,805 9,097 0.4172
#> 10 790,901 0.935 846,012 55,111 16,173 0.2935
#> 11 844,159 0.876 963,052 118,893 26,734 0.2249
#> 12 915,109 0.783 1,169,300 254,191 36,722 0.1445
#> 13 909,066 0.617 1,473,826 564,760 53,370 0.0945
#> 14 394,997 0.278 1,423,182 1,028,185 126,538 0.1231
#> Total 8,759,806 0.809 10,821,341 2,061,535 162,464 0.0788
#>
#> $`Summary Statistics for Triangle 1+2`
#> Latest Dev.To.Date Ultimate IBNR S.E CV
#> 1 941,017 1.000 941,017 0 0 0.0000
#> 2 1,046,769 0.998 1,048,579 1,810 1,851 1.0221
#> 3 1,143,452 0.996 1,148,032 4,580 7,859 1.7158
#> 4 1,269,648 0.991 1,281,370 11,722 9,545 0.8143
#> 5 1,276,125 0.987 1,292,393 16,268 12,133 0.7458
#> 6 1,360,793 0.979 1,390,091 29,298 18,913 0.6455
#> 7 1,532,180 0.970 1,578,868 46,688 22,448 0.4808
#> 8 1,670,606 0.951 1,757,679 87,073 25,913 0.2976
#> 9 1,682,455 0.914 1,840,846 158,391 33,294 0.2102
#> 10 1,932,651 0.848 2,278,572 345,921 45,253 0.1308
#> 11 2,018,355 0.748 2,699,816 681,461 72,050 0.1057
#> 12 1,947,793 0.602 3,235,135 1,287,342 112,187 0.0871
#> 13 1,682,037 0.407 4,132,660 2,450,623 222,927 0.0910
#> 14 599,322 0.162 3,691,189 3,091,867 342,127 0.1107
#> Total 20,103,203 0.710 28,316,248 8,213,045 500,607 0.0610
#>
names(fit.liab)
#> [1] "model" "Triangles" "models" "coefficients"
#> [5] "coefCov" "residCov" "fit.method" "delta"
#> [9] "int" "restrict.regMat" "mse.ay" "mse.ay.est"
#> [13] "mse.ay.proc" "mse.total" "mse.total.est" "mse.total.proc"
#> [17] "FullTriangles"
fit.liab[[1]]
#> $model
#> [1] "MCL"
#>
fit.liab$model
#> [1] "MCL"
fit.liab@model
#> [1] "MCL"
do.call("rbind",coef(fit.liab))
#> eq1_x[[1]] eq2_x[[2]]
#> [1,] 3.226968 2.2223681
#> [2,] 1.719491 1.2688125
#> [3,] 1.352471 1.1200255
#> [4,] 1.178849 1.0665251
#> [5,] 1.106443 1.0356290
#> [6,] 1.054712 1.0168421
#> [7,] 1.026122 1.0097022
#> [8,] 1.015121 1.0002188
#> [9,] 1.012075 1.0038313
#> [10,] 1.006418 0.9994269
#> [11,] 1.004538 1.0038691
#> [12,] 1.005324 0.9989420
#> [13,] 1.003456 0.9997216
vcov(fit.liab)[[1]]
#> eq1_x[[1]] eq2_x[[2]]
#> eq1_x[[1]] 0.012892793 0.001805951
#> eq2_x[[2]] 0.001805951 0.004262759
residCov(fit.liab)[[1]]
#> eq1 eq2
#> eq1 17649.406 3462.246
#> eq2 3462.246 11106.972
head(do.call("rbind",rstandard(fit.liab)))
#> eq1 eq2
#> 1 -0.93310911 -0.1775342
#> 2 -0.23597735 -0.8092400
#> 3 0.08335632 -0.3371644
#> 4 -0.02340017 -0.4127673
#> 5 -0.97850855 -0.8516139
#> 6 0.39880326 -1.3145969