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))
library(openxlsx)
## Warning: package 'openxlsx' was built under R version 4.4.1
data.cumulative <- read.xlsx("C:/Users/Admin/Desktop/chauquyct4.xlsx")
data.cumulative
## (i,j) 0 1 2 3 4
## 1 1 1.115510e+05 1.546220e+05 1.561590e+05 1.567590e+05 1.575830e+05
## 2 2 1.161630e+05 1.714490e+05 1.755020e+05 1.765330e+05 1.769890e+05
## 3 3 1.276150e+05 1.896820e+05 1.938230e+05 1.963240e+05 1.986320e+05
## 4 4 1.476590e+05 2.173420e+05 2.201230e+05 2.227310e+05 2.229160e+05
## 5 5 1.574950e+05 2.127700e+05 2.196800e+05 2.209780e+05 2.212760e+05
## 6 6 1.549690e+05 2.133520e+05 2.192010e+05 2.204690e+05 2.227510e+05
## 7 7 1.528330e+05 2.099690e+05 2.146920e+05 2.200400e+05 2.234670e+05
## 8 8 1.442230e+05 2.076440e+05 2.124430e+05 2.141080e+05 2.146610e+05
## 9 9 1.456120e+05 2.096040e+05 2.141610e+05 2.159820e+05 2.179620e+05
## 10 10 1.966950e+05 2.826210e+05 2.886760e+05 2.900360e+05 2.922060e+05
## 11 11 1.813810e+05 2.603080e+05 2.664970e+05 2.691300e+05 2.694040e+05
## 12 12 1.771680e+05 2.631300e+05 2.688480e+05 2.707870e+05 2.716240e+05
## 13 13 1.565050e+05 2.306070e+05 2.371020e+05 2.448470e+05 2.459400e+05
## 14 14 1.578390e+05 2.397230e+05 2.612130e+05 2.647550e+05 2.662687e+05
## 15 15 1.594290e+05 2.333090e+05 2.398000e+05 2.424934e+05 2.438798e+05
## 16 16 1.699900e+05 2.460190e+05 2.528699e+05 2.557101e+05 2.571721e+05
## 17 17 1.733770e+05 2.499372e+05 2.568973e+05 2.597827e+05 2.612679e+05
## 18 NA 1.441582e+00 1.027847e+00 1.011232e+00 1.005717e+00 1.004767e+00
## 5 6 7 8 9 10
## 1 158666.00000 160448.00000 1.605520e+05 160568.00000 1.606170e+05 160621.0
## 2 177269.00000 178488.00000 1.785560e+05 178620.00000 1.786210e+05 178644.0
## 3 200299.00000 202740.00000 2.038480e+05 204168.00000 2.055600e+05 205562.0
## 4 223320.00000 223447.00000 2.235660e+05 227103.00000 2.271270e+05 227276.0
## 5 223724.00000 223743.00000 2.237650e+05 223669.00000 2.236010e+05 223558.0
## 6 223958.00000 224005.00000 2.240300e+05 223975.00000 2.240480e+05 224036.0
## 7 223754.00000 223752.00000 2.235930e+05 223585.00000 2.236880e+05 223697.0
## 8 214610.00000 214564.00000 2.144840e+05 214459.00000 2.144590e+05 214478.6
## 9 220783.00000 221078.00000 2.216140e+05 221616.00000 2.218266e+05 221846.9
## 10 294531.00000 294671.00000 2.947050e+05 295295.50830 2.955762e+05 295603.2
## 11 269691.00000 269720.00000 2.699412e+05 270482.07278 2.707391e+05 270763.9
## 12 271688.00000 272364.36827 2.725877e+05 273133.91250 2.733935e+05 273418.5
## 13 247112.51410 247727.70161 2.479309e+05 248427.63687 2.486637e+05 248686.5
## 14 267538.09435 268204.13141 2.684241e+05 268961.92122 2.692175e+05 269242.2
## 15 245042.46258 245652.49669 2.458539e+05 246346.56862 2.465807e+05 246603.2
## 16 258398.13187 259041.41496 2.592538e+05 259773.31624 2.600202e+05 260044.0
## 17 262513.51760 263167.04595 2.633829e+05 263910.60387 2.641614e+05 264185.6
## 18 1.00249 1.00082 1.002004e+00 1.00095 1.000091e+00 NA
## R
## 1 NA
## 2 NA
## 3 NA
## 4 NA
## 5 NA
## 6 NA
## 7 0.00000
## 8 19.61431
## 9 230.91171
## 10 898.19002
## 11 1043.90026
## 12 1730.50305
## 13 2746.48483
## 14 4487.16478
## 15 6803.24822
## 16 14024.98578
## 17 90808.58424
## 18 122793.58721
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)
M <- MackChainLadder(tri, est.sigma="Mack")
M
## MackChainLadder(Triangle = tri, est.sigma = "Mack")
##
## Latest Dev.To.Date Ultimate IBNR Mack.S.E CV(IBNR)
## 1 160,621.0 22.7 7,072.9 -153,548 0 0
## 2 178,644.0 22.7 7,866.5 -170,777 0 0
## 3 205,562.0 22.7 9,051.8 -196,510 0 0
## 4 227,276.0 22.7 10,008.0 -217,268 0 0
## 5 223,558.0 22.7 9,844.3 -213,714 0 0
## 6 224,036.0 22.7 9,865.3 -214,171 0 0
## 8 19.6 1.0 19.6 0 24,914 Inf
## 9 230.9 1.0 230.9 0 25,370 Inf
## 10 898.2 1.0 898.2 0 29,641 Inf
## 11 1,043.9 1.0 1,043.9 0 28,254 Inf
## 12 1,730.5 1.0 1,730.5 0 28,405 Inf
## 13 2,746.5 1.0 2,746.5 0 26,980 Inf
## 14 4,487.2 1.0 4,487.2 0 28,168 Inf
## 15 6,803.2 1.0 6,803.2 0 26,858 Inf
## 16 14,025.0 1.0 14,025.0 0 27,641 Inf
## 17 90,808.6 1.0 90,808.6 0 27,882 Inf
## 18 122,793.6 1.0 122,793.6 0 NA NA
##
## Totals
## Latest: 1,465,284.17
## Dev: 4.90
## Ultimate: 299,296.06
## IBNR: -1,165,988.11
## Mack.S.E 122,425.82
## CV(IBNR): -0.10
plot(M)
plot(M, lattice=TRUE)
CDR(M)
## IBNR CDR(1)S.E. Mack.S.E.
## 1 0.00 0.000000 0.00000
## 2 0.00 0.000000 0.00000
## 3 0.00 0.000000 0.00000
## 4 0.00 0.000000 0.00000
## 5 0.00 0.000000 0.00000
## 6 0.00 0.000000 0.00000
## 7 -223697.00 0.000000 0.00000
## 8 -214439.39 4.943072 54.06614
## 9 -221385.09 58.193981 627.44614
## 10 -293806.81 226.376093 2167.73740
## 11 -268676.10 263.080090 2610.76415
## 12 -269957.50 436.145991 4310.71399
## 13 -243193.52 692.222815 7114.02485
## 14 -260267.84 1130.950501 11248.22390
## 15 -232996.75 1715.202131 17683.77697
## 16 -231994.01 3541.741042 35663.77222
## 17 -82568.42 23043.488331 229433.86890
## 18 NA NA NA
## Total NA NA NA
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 -223697 0 0 0 0 0 0
## 8 -214439 5 54 0 0 0 0
## 9 -221385 58 1 625 0 0 0
## 10 -293807 226 2 7 2156 0 0
## 11 -268676 263 4 8 16 2597 0
## 12 -269957 436 4 15 27 29 4288
## 13 -243194 692 11 22 44 46 59
## 14 -260268 1131 19 38 70 77 97
## 15 -232997 1715 31 59 108 114 149
## 16 -231994 3542 103 123 223 239 303
## 17 -82568 23043 1471 952 1451 1554 1983
## 18 NA NA 1222804 936244 412705 225565 210805
## Total NA NA 1222809 936311 413294 226813 213012
## CDR(7)S.E. CDR(8)S.E. CDR(9)S.E. CDR(10)S.E. CDR(11)S.E. CDR(12)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 0
## 9 0 0 0 0 0 0
## 10 0 0 0 0 0 0
## 11 0 0 0 0 0 0
## 12 0 0 0 0 0 0
## 13 7080 0 0 0 0 0
## 14 122 11190 0 0 0 0
## 15 186 238 17596 0 0 0
## 16 385 490 606 35474 0 0
## 17 2477 3187 3926 5707 228108 0
## 18 196032 74225 207956 85012 25420 144545735
## Total 199790 89087 216650 122492 276417 144545735
## CDR(13)S.E. Mack.S.E.
## 1 0 0
## 2 0 0
## 3 0 0
## 4 0 0
## 5 0 0
## 6 0 0
## 7 0 0
## 8 0 54
## 9 0 627
## 10 0 2168
## 11 0 2611
## 12 0 4311
## 13 0 7114
## 14 0 11248
## 15 0 17684
## 16 0 35664
## 17 0 229434
## 18 0 NA
## Total 0 NA