Nhiệm vụ Tuần 5
Quỳnh Hương
18:10:22, 02 - 07 - 2025
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)
data <- read_excel("D:/HK2_MHRRBH_TDP/r_2725.xlsx")## New names:
## • `` -> `...1`tri <- as.triangle(as.matrix(data))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)
dim(tri)## [1] 17 18tri <- tri[, 2:17]
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 24,001 1.000 24,001 0.00 0.00 NaN
## 2 24,550 1.000 24,550 0.00 0.00 NaN
## 3 25,732 1.000 25,741 9.01 2.53 0.281
## 4 26,167 0.999 26,187 20.10 16.89 0.841
## 5 26,735 0.996 26,852 116.54 157.27 1.349
## 6 26,959 0.992 27,181 222.15 207.16 0.933
## 7 25,723 0.986 26,084 360.72 261.92 0.726
## 8 30,302 0.985 30,770 468.13 292.25 0.624
## 9 28,948 0.978 29,600 652.27 390.57 0.599
## 10 29,830 0.967 30,837 1,007.01 501.90 0.498
## 11 27,480 0.965 28,489 1,009.16 486.33 0.482
## 12 29,183 0.954 30,587 1,403.80 807.01 0.575
## 13 24,210 0.942 25,700 1,490.46 794.02 0.533
## 14 24,029 0.919 26,150 2,120.73 1,239.34 0.584
## 15 22,603 0.902 25,072 2,469.24 1,350.08 0.547
## 16 20,111 0.856 23,506 3,394.74 1,463.40 0.431
## 17 12,539 0.566 22,145 9,606.35 1,594.09 0.166
##
## Totals
## Latest: 429,102.00
## Dev: 0.95
## Ultimate: 453,452.39
## IBNR: 24,350.39
## Mack.S.E 3,817.86
## CV(IBNR): 0.16plot(M)
plot(M, lattice=TRUE)
CDR(M)## IBNR CDR(1)S.E. Mack.S.E.
## 1 0.000000 0.000000 0.000000
## 2 0.000000 0.000000 0.000000
## 3 9.013145 2.530036 2.530036
## 4 20.096491 16.721116 16.892351
## 5 116.543797 156.395592 157.268485
## 6 222.147248 137.646352 207.155985
## 7 360.721404 171.173937 261.915348
## 8 468.126795 70.312710 292.249649
## 9 652.270932 271.623791 390.570914
## 10 1007.005144 310.030007 501.904517
## 11 1009.155632 104.665239 486.332479
## 12 1403.799022 632.580551 807.013544
## 13 1490.464164 315.021526 794.020254
## 14 2120.725025 948.846160 1239.340015
## 15 2469.239251 604.145133 1350.077556
## 16 3394.735373 671.295281 1463.398884
## 17 9606.345100 735.785256 1594.093764
## Total 24350.388522 2185.909760 3817.858242round(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 9 3 0 0 0 0 0
## 4 20 17 2 0 0 0 0
## 5 117 156 16 2 0 0 0
## 6 222 138 154 16 2 0 0
## 7 361 171 131 148 15 2 0
## 8 468 70 185 142 161 17 2
## 9 652 272 62 178 137 156 16
## 10 1007 310 274 59 180 139 158
## 11 1009 105 293 260 53 171 131
## 12 1404 633 104 302 269 53 177
## 13 1490 315 572 88 273 243 45
## 14 2121 949 315 575 86 274 244
## 15 2469 604 925 305 561 82 267
## 16 3395 671 581 891 293 541 77
## 17 9606 736 648 561 862 283 523
## Total 24350 2186 1833 1558 1326 902 786
## 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 2 0 0 0 0 0
## 10 17 2 0 0 0 0
## 11 150 16 2 0 0 0
## 12 136 156 16 2 0 0
## 13 160 123 141 15 2 0
## 14 44 161 124 142 15 2
## 15 238 42 156 120 139 15
## 16 257 229 40 151 116 134
## 17 73 249 222 38 146 112
## Total 526 477 367 270 245 180
## CDR(13)S.E. CDR(14)S.E. CDR(15)S.E. CDR(16)S.E. Mack.S.E.
## 1 0 0 0 0 0
## 2 0 0 0 0 0
## 3 0 0 0 0 3
## 4 0 0 0 0 17
## 5 0 0 0 0 157
## 6 0 0 0 0 207
## 7 0 0 0 0 262
## 8 0 0 0 0 292
## 9 0 0 0 0 391
## 10 0 0 0 0 502
## 11 0 0 0 0 486
## 12 0 0 0 0 807
## 13 0 0 0 0 794
## 14 0 0 0 0 1239
## 15 2 0 0 0 1350
## 16 14 2 0 0 1463
## 17 129 14 2 0 1594
## Total 130 14 2 0 3818# Áp dụng mô hình Mack Chain-Ladder
library(ChainLadder)
M <- MackChainLadder(tri, est.sigma = "Mack")
# In kết quả mô hình
M## MackChainLadder(Triangle = tri, est.sigma = "Mack")
##
## Latest Dev.To.Date Ultimate IBNR Mack.S.E CV(IBNR)
## 1 24,001 1.000 24,001 0.00 0.00 NaN
## 2 24,550 1.000 24,550 0.00 0.00 NaN
## 3 25,732 1.000 25,741 9.01 2.53 0.281
## 4 26,167 0.999 26,187 20.10 16.89 0.841
## 5 26,735 0.996 26,852 116.54 157.27 1.349
## 6 26,959 0.992 27,181 222.15 207.16 0.933
## 7 25,723 0.986 26,084 360.72 261.92 0.726
## 8 30,302 0.985 30,770 468.13 292.25 0.624
## 9 28,948 0.978 29,600 652.27 390.57 0.599
## 10 29,830 0.967 30,837 1,007.01 501.90 0.498
## 11 27,480 0.965 28,489 1,009.16 486.33 0.482
## 12 29,183 0.954 30,587 1,403.80 807.01 0.575
## 13 24,210 0.942 25,700 1,490.46 794.02 0.533
## 14 24,029 0.919 26,150 2,120.73 1,239.34 0.584
## 15 22,603 0.902 25,072 2,469.24 1,350.08 0.547
## 16 20,111 0.856 23,506 3,394.74 1,463.40 0.431
## 17 12,539 0.566 22,145 9,606.35 1,594.09 0.166
##
## Totals
## Latest: 429,102.00
## Dev: 0.95
## Ultimate: 453,452.39
## IBNR: 24,350.39
## Mack.S.E 3,817.86
## CV(IBNR): 0.16# Xem rủi ro quy trình theo từng dòng (row) tại cột cuối
M$Mack.ProcessRisk[, ncol(tri)]## 1 2 3 4 5 6
## 0.000000 0.000000 2.045289 14.504982 139.645606 185.522298
## 7 8 9 10 11 12
## 238.262522 262.027257 358.221304 463.883900 452.297887 760.230659
## 13 14 15 16 17
## 756.302939 1189.278813 1299.664076 1414.254553 1545.854277# Xem tổng rủi ro quy trình (process risk) tại cột cuối
M$Total.ProcessRisk[ncol(tri)]## 17
## 3061.19# Xem rủi ro tham số (parameter risk) theo từng dòng tại cột cuối
M$Mack.ParameterRisk[, ncol(tri)]## 1 2 3 4 5 6 7
## 0.000000 0.000000 1.489253 8.657772 72.335891 92.168755 108.768654
## 8 9 10 11 12 13 14
## 129.427870 155.637838 191.624300 178.734163 270.777041 241.814034 348.682631
## 15 16 17
## 365.489666 376.058978 389.190802# Xem tổng rủi ro tham số tại cột cuối
M$Total.ParameterRisk[ncol(tri)]## [1] 2281.482# Vẽ đồ thị trực quan hóa
plot(M)
plot(M, lattice = TRUE)
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