# Nạp thư viện
library(ChainLadder)
## Warning: package 'ChainLadder' was built under R version 4.3.3
##
## 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(readxl)
## Warning: package 'readxl' was built under R version 4.3.3
##############################
######### loading data
##############################
# Đọc dữ liệu từ file Excel (sheet mặc định là đầu tiên)
data.cumulative <- read_xlsx("D:/Downloads/datamhrrbh.xlsx", sheet = 1)
# Chuyển đổi sang dạng ma trận và triangle
tri <- as.triangle(as.matrix(data.cumulative))
# Đặt tên chiều cho triangle (origin, development period)
dimnames(tri) <- list(origin = 1:nrow(tri), dev = 0:(ncol(tri)-1))
##############################
######### Plot dữ liệu tam giác
##############################
units1 <- 1000
ylab1 <- paste("Claims (x", units1, ")", sep = "")
title1 <- "Cumulative Claims Development"
# Biểu đồ thường và lattice
plot(tri / units1, ylab = ylab1, main = title1)
plot(tri / units1, lattice = TRUE, ylab = ylab1, main = title1)
##############################
######### Mack ChainLadder Model
##############################
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 NaN
## 2 178,644 1.000 178,644 0.0 0 NaN
## 3 205,562 1.000 205,562 0.0 0 NaN
## 4 227,276 1.000 227,276 0.0 0 NaN
## 5 223,558 1.000 223,558 0.0 0 NaN
## 6 224,036 1.000 224,036 0.0 0 NaN
## 7 223,697 1.000 223,697 0.0 65 Inf
## 8 214,459 1.000 214,479 19.6 533 27.194
## 9 221,616 0.999 221,847 230.9 1,335 5.781
## 10 294,705 0.997 295,688 982.8 1,635 1.663
## 11 269,720 0.996 270,774 1,054.4 1,933 1.833
## 12 271,688 0.994 273,429 1,741.1 2,274 1.306
## 13 245,940 0.989 248,696 2,756.2 2,444 0.887
## 14 264,755 0.983 269,253 4,497.6 3,314 0.737
## 15 239,800 0.972 246,613 6,812.8 5,500 0.807
## 16 246,019 0.946 260,054 14,035.1 10,019 0.714
## 17 173,377 0.656 264,196 90,818.9 237,321 2.613
##
## Totals
## Latest: 3,885,473.00
## Dev: 0.97
## Ultimate: 4,008,422.42
## IBNR: 122,949.42
## Mack.S.E 237,772.61
## CV(IBNR): 1.93
# Biểu đồ kết quả Mack
plot(M)
plot(M, lattice = TRUE)
##############################
######### Claims Development Result (CDR)
##############################
# Tổng thể
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 9.00000 65.76116 65.76116
## 8 19.61431 533.67609 537.44492
## 9 768.91171 1229.98334 1344.84600
## 10 1016.76204 505.89594 1650.01477
## 11 1083.42700 1168.20567 1946.50228
## 12 1805.13299 1205.64894 2287.95224
## 13 3849.15325 1174.70277 2457.36392
## 14 8039.63236 2143.51038 3334.39163
## 15 13303.83564 4521.15654 5517.39145
## 16 90064.09575 8333.11120 10073.47213
## 17 264178.85523 141527.42650 141888.31426
## Total 384138.42027 141987.64772 142669.05448
# Chi tiết theo từng kỳ phát triển
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 9 66 0 0 0 0 0
## 8 20 534 64 0 0 0 0
## 9 769 1230 540 64 0 0 0
## 10 1017 506 1436 631 75 0 0
## 11 1083 1168 476 1356 595 71 0
## 12 1805 1206 1169 468 1355 595 71
## 13 3849 1175 1139 1101 436 1280 562
## 14 8040 2144 1222 1182 1144 450 1331
## 15 13304 4521 2033 1157 1121 1085 424
## 16 90064 8333 4639 2085 1185 1148 1113
## 17 264179 141527 8362 4663 2094 1189 1154
## Total 384138 141988 10762 6270 3856 2924 2512
## 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 67 0 0 0 0 0
## 14 585 70 0 0 0 0
## 15 1265 556 66 0 0 0
## 16 434 1298 570 68 0 0
## 17 1118 439 1305 573 68 0
## Total 2034 1598 1444 578 68 0
## Mack.S.E.
## 1 0
## 2 0
## 3 0
## 4 0
## 5 0
## 6 0
## 7 66
## 8 537
## 9 1345
## 10 1650
## 11 1947
## 12 2288
## 13 2457
## 14 3334
## 15 5517
## 16 10073
## 17 141888
## Total 142669