library(ChainLadder)
## Warning: package 'ChainLadder' was built under R version 4.4.3
##
## Welcome to ChainLadder version 0.2.20
##
##
## To cite package 'ChainLadder' in publications use:
##
## Gesmann M, Murphy D, Zhang Y, Carrato A, Wuthrich M, Concina F, Dal
## Moro E (2025). _ChainLadder: Statistical Methods and Models for
## Claims Reserving in General Insurance_. R package version 0.2.20,
## <https://CRAN.R-project.org/package=ChainLadder>.
##
## To suppress this message use:
## suppressPackageStartupMessages(library(ChainLadder))
##############################
######### loading data
##############################
data.cumulative <- read.csv("C:/Users/TAM NHU/Downloads/Baohiem.csv", header=FALSE, )
data.cumulative
## V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11
## 1 111551 154622 156159 156759 157583 158666 160448 160552 160568 160617 160621
## 2 116163 171449 175502 176533 176989 177269 178488 178556 178620 178621 178644
## 3 127615 189682 193823 196324 198632 200299 202740 203848 204168 205560 205562
## 4 147659 217342 220123 222731 222916 223320 223447 223566 227103 227127 227276
## 5 157495 212770 219680 220978 221276 223724 223743 223765 223669 223601 223558
## 6 154969 213352 219201 220469 222751 223958 224005 224030 223975 224048 224036
## 7 152833 209969 214692 220040 223467 223754 223752 223593 223585 223688 223697
## 8 144223 207644 212443 214108 214661 214610 214564 214484 214459 214459 NA
## 9 145612 209604 214161 215982 217962 220783 221078 221614 221616 NA NA
## 10 196695 282621 288676 290036 292206 294531 294671 294705 NA NA NA
## 11 181381 260308 266497 269130 269404 269691 269720 NA NA NA NA
## 12 177168 263130 268848 270787 271624 271688 NA NA NA NA NA
## 13 156505 230607 237102 244847 245940 NA NA NA NA NA NA
## 14 157839 239723 261213 264755 NA NA NA NA NA NA NA
## 15 159429 233309 239800 NA NA NA NA NA NA NA NA
## 16 169990 246019 NA NA NA NA NA NA NA NA NA
## 17 173377 NA NA NA NA NA NA NA NA NA NA
##############################
######### bringing data in appropriate form and plot
##############################
tri <- as.triangle(as.matrix(data.cumulative))
dimnames(tri)=list(origin=1:nrow(tri), dev=1:ncol(tri))
units1 <- 1000
ylab1 <- paste(units1)
title1 <- ""
plot(tri/units1, lattice=TRUE, ylab=ylab1, main=title1)
plot(tri/units1, ylab=ylab1, main=title1)
##############################
######### Mack ChainLadder
##############################
M <- MackChainLadder(tri, est.sigma="Mack")
M
## MackChainLadder(Triangle = tri, est.sigma = "Mack")
##
## Latest Dev.To.Date Ultimate IBNR Mack.S.E CV(IBNR)
## 1 160,621 1.000 160,621 0.0 0.0 NaN
## 2 178,644 1.000 178,644 0.0 0.0 NaN
## 3 205,562 1.000 205,562 0.0 0.0 NaN
## 4 227,276 1.000 227,276 0.0 0.0 NaN
## 5 223,558 1.000 223,558 0.0 0.0 NaN
## 6 224,036 1.000 224,036 0.0 0.0 NaN
## 7 223,697 1.000 223,697 0.0 0.0 NaN
## 8 214,459 1.000 214,479 19.6 63.4 3.234
## 9 221,616 0.999 221,847 230.9 543.3 2.353
## 10 294,705 0.997 295,603 898.2 1,582.0 1.761
## 11 269,720 0.996 270,764 1,043.9 1,573.6 1.507
## 12 271,688 0.994 273,419 1,730.5 1,957.5 1.131
## 13 245,940 0.989 248,686 2,746.5 2,168.8 0.790
## 14 264,755 0.983 269,242 4,487.2 2,563.5 0.571
## 15 239,800 0.972 246,603 6,803.2 3,169.1 0.466
## 16 246,019 0.946 260,044 14,025.0 5,663.2 0.404
## 17 173,377 0.656 264,186 90,808.6 10,121.0 0.111
##
## Totals
## Latest: 3,885,473.00
## Dev: 0.97
## Ultimate: 4,008,266.59
## IBNR: 122,793.59
## Mack.S.E 13,941.87
## CV(IBNR): 0.11
plot(M)
plot(M, lattice=TRUE)
##############################
######### claims development result
##############################
CDR(M)
## IBNR CDR(1)S.E. Mack.S.E.
## 1 0.00000 0.00000 0.00000
## 2 0.00000 0.00000 0.00000
## 3 0.00000 0.00000 0.00000
## 4 0.00000 0.00000 0.00000
## 5 0.00000 0.00000 0.00000
## 6 0.00000 0.00000 0.00000
## 7 0.00000 0.00000 0.00000
## 8 19.61431 63.43912 63.43912
## 9 230.91171 539.46869 543.26392
## 10 898.19002 1449.62920 1582.02974
## 11 1043.90026 499.00197 1573.61113
## 12 1730.50305 1170.60166 1957.54161
## 13 2746.48483 1140.91743 2168.84180
## 14 4487.16478 1224.62884 2563.46434
## 15 6803.24822 2034.38637 3169.05098
## 16 14024.98578 4639.36377 5663.19036
## 17 90808.58424 8367.41032 10120.98178
## Total 122793.58721 10778.17359 13941.86695
round(CDR(M, dev="all"),0)
## IBNR CDR(1)S.E. CDR(2)S.E. CDR(3)S.E. CDR(4)S.E. CDR(5)S.E. CDR(6)S.E.
## 1 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0
## 3 0 0 0 0 0 0 0
## 4 0 0 0 0 0 0 0
## 5 0 0 0 0 0 0 0
## 6 0 0 0 0 0 0 0
## 7 0 0 0 0 0 0 0
## 8 20 63 0 0 0 0 0
## 9 231 539 64 0 0 0 0
## 10 898 1450 629 75 0 0 0
## 11 1044 499 1367 594 71 0 0
## 12 1731 1171 490 1366 593 70 0
## 13 2746 1141 1101 455 1290 560 67
## 14 4487 1225 1183 1143 469 1342 583
## 15 6803 2034 1157 1121 1084 443 1275
## 16 14025 4639 2085 1185 1148 1112 452
## 17 90809 8367 4666 2095 1189 1153 1117
## Total 122794 10778 6277 3854 2919 2508 2034
## CDR(7)S.E. CDR(8)S.E. CDR(9)S.E. CDR(10)S.E. CDR(11)S.E. Mack.S.E.
## 1 0 0 0 0 0 0
## 2 0 0 0 0 0 0
## 3 0 0 0 0 0 0
## 4 0 0 0 0 0 0
## 5 0 0 0 0 0 0
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 63
## 9 0 0 0 0 0 543
## 10 0 0 0 0 0 1582
## 11 0 0 0 0 0 1574
## 12 0 0 0 0 0 1958
## 13 0 0 0 0 0 2169
## 14 69 0 0 0 0 2563
## 15 554 66 0 0 0 3169
## 16 1309 569 68 0 0 5663
## 17 454 1316 572 68 0 10121
## Total 1603 1452 577 68 0 13942