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Last data update: 2014.03.03 |
Claims Reserving under the Double Chain Ladder ModelDescriptionThis package provides functions for statistical modelling and forecasting in claims reserving in non-life insurance under the Double Chain Ladder framework by Martinez-Miranda, Nielsen and Verrall (2012). Using specific functions, the user will be able generate plots to visualize and gain intuition about the data (run-off triangles), break down classical chain ladder under the DCL model, visualize the underlying delay function and the inflation, introduce expert knowledge about the severity inflation, the zero-claims etc. Besides a validation exercise can be performed through a back-test on the data. Details
Author(s)M.D. Martinez-Miranda, J.P. Nielsen and R. Verrall Maintainer: Maria Dolores Martinez-Miranda <mmiranda@ugr.es> ReferencesMartinez-Miranda M.D., Nielsen B, Nielsen J.P and Verrall, R. (2011) Cash flow simulation for a model of outstanding liabilities based on claim amounts and claim numbers. Astin Bulletin, 41/1, 107-129. Martinez-Miranda, M.D., Nielsen, J.P. and Verrall, R. (2012) Double Chain Ladder. Astin Bulletin, 42/1, 59-76. Martinez-Miranda, M.D., Nielsen, J.P. and Verrall, R. (2013) Double Chain Ladder and Bornhuetter-Ferguson. North American Actuarial Journal, 17(2), 101-113. Martinez-Miranda, M.D., Nielsen, J.P., Verrall, R. and Wuthrich, M.V. (2013) Double Chain Ladder, Claims Development Inflation and Zero Claims. Scandinavian Actuarial Journal. In press. See more at http://www.cassknowledge.com/research/article/double-chain-ladder-cass-knowledge Examplesdata(NtriangleDCL) data(XtriangleDCL) # Classical chain ladder parameters my.clm.par<-clm(XtriangleDCL) Plot.clm.par(my.clm.par) # Estimation of the DCL parameters (break-down of the chain ladder parameters) my.dcl.par<-dcl.estimation(XtriangleDCL,NtriangleDCL) Plot.dcl.par(my.dcl.par) # DCL Predictions by diagonals (future calendar years) # Splitting the chain ladder reserve into RBNR and IBNR claims (ignoring the tail) preds.dcl.diag<-dcl.predict(my.dcl.par,Model=0,Tail=FALSE,num.dec=0) # Full cashflow considering the tail (only the variance process) # Below only B=200 simulations for faster calculations in the example boot1<-dcl.boot(dcl.par=my.dcl.par,Ntriangle=NtriangleDCL,boot.type=1,B=200) Plot.cashflow(boot1) Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(DCL)
Loading required package: lattice
Loading required package: latticeExtra
Loading required package: RColorBrewer
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/DCL/DCL-package.Rd_%03d_medium.png", width=480, height=480)
> ### Name: DCL-package
> ### Title: Claims Reserving under the Double Chain Ladder Model
> ### Aliases: DCL-package DCL
> ### Keywords: package package
>
> ### ** Examples
>
> data(NtriangleDCL)
> data(XtriangleDCL)
>
> # Classical chain ladder parameters
> my.clm.par<-clm(XtriangleDCL)
> Plot.clm.par(my.clm.par)
>
> # Estimation of the DCL parameters (break-down of the chain ladder parameters)
> my.dcl.par<-dcl.estimation(XtriangleDCL,NtriangleDCL)
delay.par delay.prob inflation severity.mean severity.var
1 0.3649 0.3649 1.0000 208.4910 2055848.1
2 0.2924 0.2924 0.7562 157.6619 1175628.8
3 0.1119 0.1119 0.7350 153.2415 1110629.4
4 0.0839 0.0839 0.8908 185.7203 1631305.5
5 0.0630 0.0630 0.7840 163.4627 1263728.0
6 0.0332 0.0332 0.7791 162.4267 1247760.4
7 0.0245 0.0245 0.6605 137.7131 896947.6
8 0.0121 0.0121 0.7370 153.6665 1116798.1
9 0.0158 0.0142 0.6990 145.7439 1004609.0
10 -0.0012 0.0000 0.8198 170.9139 1381564.2
mean.factor mean.factor.adj variance.factor
1 208.3748 208.491 2055848
> Plot.dcl.par(my.dcl.par)
>
> # DCL Predictions by diagonals (future calendar years)
> # Splitting the chain ladder reserve into RBNR and IBNR claims (ignoring the tail)
> preds.dcl.diag<-dcl.predict(my.dcl.par,Model=0,Tail=FALSE,num.dec=0)
Future.years rbns ibnr total clm
1 1 1256744 97114 1353858 1353858
2 2 671784 82396 754180 754180
3 3 453470 35142 488612 488612
4 4 292068 25975 318043 318043
5 5 164895 19716 184611 184611
6 6 103780 11242 115023 115023
7 7 54819 8326 63145 63145
8 8 31252 4561 35813 35813
9 9 -2325 4820 2494 2494
10 10 0 0 0 NA
11 11 0 0 0 NA
12 12 0 0 0 NA
13 13 0 0 0 NA
14 14 0 0 0 NA
15 15 0 0 0 NA
16 16 0 0 0 NA
17 17 0 0 0 NA
18 18 0 0 0 NA
19 Tot. 3026488 289292 3315779 3315779
>
> # Full cashflow considering the tail (only the variance process)
> # Below only B=200 simulations for faster calculations in the example
> boot1<-dcl.boot(dcl.par=my.dcl.par,Ntriangle=NtriangleDCL,boot.type=1,B=200)
[1] "Please wait, simulating the distribution..."
[1] "Done!"
period rbns mean.rbns sd.rbns Q1.rbns Q5.rbns Q50.rbns
1 1 1260907.90 1254024.11 105004.46 1026486.02 1091338.71 1243532.96
2 2 672017.58 668205.97 73202.33 541519.84 560011.17 661768.98
3 3 453360.52 455194.66 60680.81 306498.92 367068.24 454791.61
4 4 292539.65 295308.10 45535.58 203573.14 223146.24 299111.25
5 5 164970.41 160199.00 35490.54 99357.82 110462.32 157648.25
6 6 103125.19 106893.91 29993.28 55080.79 63542.98 104455.29
7 7 54037.12 54300.76 20731.50 17818.01 27209.22 50904.57
8 8 30396.54 30711.46 16157.17 6576.01 9170.95 28523.96
9 9 0.00 0.00 0.00 0.00 0.00 0.00
10 10 0.00 0.00 0.00 0.00 0.00 0.00
11 11 0.00 0.00 0.00 0.00 0.00 0.00
12 12 0.00 0.00 0.00 0.00 0.00 0.00
13 13 0.00 0.00 0.00 0.00 0.00 0.00
14 14 0.00 0.00 0.00 0.00 0.00 0.00
15 15 0.00 0.00 0.00 0.00 0.00 0.00
16 16 0.00 0.00 0.00 0.00 0.00 0.00
17 17 0.00 0.00 0.00 0.00 0.00 0.00
18 18 0.00 0.00 0.00 0.00 0.00 0.00
19 Tot. 3031354.91 3024837.97 163755.56 2704880.12 2753364.43 3013070.80
Q95.rbns Q99.rbns
1 1415356.90 1498929.81
2 812379.79 841874.78
3 557529.72 590484.90
4 376078.57 406102.16
5 221787.16 270586.65
6 163249.64 183163.15
7 92642.67 116451.16
8 59323.43 80657.39
9 0.00 0.00
10 0.00 0.00
11 0.00 0.00
12 0.00 0.00
13 0.00 0.00
14 0.00 0.00
15 0.00 0.00
16 0.00 0.00
17 0.00 0.00
18 0.00 0.00
19 3319858.11 3386524.39
period ibnr mean.ibnr sd.ibnr Q1.ibnr Q5.ibnr Q50.ibnr Q95.ibnr
1 1 97168.11 96542.05 25897.70 46003.91 57971.83 94261.64 143646.22
2 2 82620.00 83517.04 24410.77 35892.02 50329.20 78868.13 127479.47
3 3 35505.74 34707.58 15631.32 8047.82 12540.78 33560.67 62144.90
4 4 26503.46 25012.80 13598.91 3187.32 5837.98 23377.89 50541.90
5 5 20353.21 18227.37 11177.56 2444.12 4210.69 15862.74 39424.63
6 6 11970.64 11093.49 9342.69 285.08 992.24 9356.03 29214.63
7 7 9074.00 8869.92 9040.84 112.23 575.42 6373.35 27511.50
8 8 5411.50 4438.65 5765.12 6.58 75.32 2298.49 16011.26
9 9 5459.61 5525.87 6447.23 4.04 39.83 3328.08 18911.89
10 10 1119.08 885.59 2321.49 0.00 0.00 18.60 4889.88
11 11 580.33 351.19 1118.39 0.00 0.00 0.00 2181.40
12 12 355.37 180.79 791.18 0.00 0.00 0.00 720.69
13 13 210.61 120.73 633.51 0.00 0.00 0.00 410.43
14 14 116.42 66.36 356.25 0.00 0.00 0.00 111.91
15 15 64.70 52.33 563.38 0.00 0.00 0.00 1.34
16 16 32.12 3.89 51.38 0.00 0.00 0.00 0.00
17 17 12.77 28.50 396.13 0.00 0.00 0.00 0.00
18 18 0.00 0.00 0.00 0.00 0.00 0.00 0.00
19 Tot. 296557.68 289624.13 47459.51 187287.43 214930.07 289026.85 367682.22
Q99.ibnr
1 150301.60
2 140432.61
3 79840.14
4 60614.33
5 53131.71
6 38438.57
7 39796.21
8 25042.29
9 27266.15
10 9192.56
11 6301.31
12 4504.21
13 3224.56
14 2376.80
15 626.23
16 17.63
17 4.19
18 0.00
19 382867.70
period total mean.total sd.total Q1.total Q5.total Q50.total
1 1 1358076.01 1350566.16 106557.11 1144756.20 1186746.46 1343071.09
2 2 754637.59 751723.01 76043.31 600391.03 629328.70 754481.37
3 3 488866.26 489902.24 62366.07 355729.65 389440.40 492572.52
4 4 319043.11 320320.90 47346.45 220782.91 252131.55 319571.36
5 5 185323.62 178426.37 36965.27 114982.31 123092.21 176181.30
6 6 115095.83 117987.40 32651.87 58519.03 70413.28 115493.90
7 7 63111.11 63170.69 22621.66 18664.37 33487.87 60335.24
8 8 35808.04 35150.11 17206.09 7957.95 11957.73 31817.46
9 9 5459.61 5525.87 6447.23 4.04 39.83 3328.08
10 10 1119.08 885.59 2321.49 0.00 0.00 18.60
11 11 580.33 351.19 1118.39 0.00 0.00 0.00
12 12 355.37 180.79 791.18 0.00 0.00 0.00
13 13 210.61 120.73 633.51 0.00 0.00 0.00
14 14 116.42 66.36 356.25 0.00 0.00 0.00
15 15 64.70 52.33 563.38 0.00 0.00 0.00
16 16 32.12 3.89 51.38 0.00 0.00 0.00
17 17 12.77 28.50 396.13 0.00 0.00 0.00
18 18 0.00 0.00 0.00 0.00 0.00 0.00
19 Tot. 3327912.59 3314462.11 168876.47 2984460.46 3065993.14 3313740.53
Q95.total Q99.total
1 1513007.91 1606208.48
2 881191.49 953440.57
3 596907.44 634725.41
4 403456.68 429559.71
5 247106.60 288231.85
6 178286.93 203116.64
7 99792.70 140743.90
8 62456.13 83142.40
9 18911.89 27266.15
10 4889.88 9192.56
11 2181.40 6301.31
12 720.69 4504.21
13 410.43 3224.56
14 111.91 2376.80
15 1.34 626.23
16 0.00 17.63
17 0.00 4.19
18 0.00 0.00
19 3589903.67 3683957.27
> Plot.cashflow(boot1)
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> dev.off()
null device
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Created & Maintained by Osamu Ogasawara (osamu.ogasawara@gmail.com) and