| data.loss.VNJ {apc} | R Documentation |
Motor data
Description
Function that organises motor data in apc.data.list format.
The data set is taken from tables 1,2 of Verrall, Nielsen and Jessen (2010). Data from Codan, Danish subsiduary of Royal & Sun Alliance. It is a portfolio of third party liability from motor policies. The time units are in years. There are two run-off triangles: "response" (X) is paid amounts (units not reported) "counts" (N) is number of reported claims.
Data also analysed in e.g. Martinez Miranda, Nielsen, Nielsen and Verrall (2011) and Kuang, Nielsen, Nielsen (2015).
The data set is in "CL"-format.
At present apc.package does not have functions for either forecasting or for exploiting the counts.
For this one can with advantage use the DCL.package.
Usage
data.loss.VNJValue
The value is a list in apc.data.list format.
response |
vector of paid amounts, X |
counts |
vector of number of reported claims, N |
dose |
NULL. |
data.format |
logical. Equal to "CL.vector.by.row". Data organised in vectors. |
age1 |
numeric. Equal to 1. |
per1 |
NULL. Not needed when data.format="CL" |
coh1 |
numeric. Equal to 1. |
unit |
numeric. Equal to 1. |
per.zero |
NULL. Not needed when data.format="CL" |
per.max |
NULL. Not needed when data.format="CL" |
time.adjust |
0. Thus age=1 in cohort=1 corresponds to period=1+1-1+0=1. |
label |
character. "loss VNJ". |
Author(s)
Bent Nielsen <bent.nielsen@nuffield.ox.ac.uk> 18 Mar 2015 updated 4 Jan 2016
Source
Tables 1,2 of Verrall, Nielsen and Jessen (2010).
References
Verrall R, Nielsen JP, Jessen AH (2010) Prediction of RBNS and IBNR claims using claim amounts and claim counts ASTIN Bulletin 40, 871-887
Martinez 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, 107-129
Kuang D, Nielsen B, Nielsen JP (2015) The geometric chain-ladder Scandinavian Acturial Journal 2015, 278-300.
See Also
General description of apc.data.list format.
Examples
#########################
## It is convient to construct a data variable
data <- data.loss.VNJ()
## To see the content of the data
data
#########################
# Fit chain-ladder model
fit.ac <- apc.fit.model(data,"poisson.response","AC")
fit.ac$coefficients.canonical
id.ac <- apc.identify(fit.ac)
id.ac$coefficients.dif
#########################
# Compare output with table 7.2 in
# Kuang D, Nielsen B, Nielsen JP (2015)
# Estimate Std. Error z value Pr(>|z|)
# level 13.07063963 0.0000000000 Inf 0.000000e+00
# D_age_2 -0.06543495 0.0006018694 -108.71950 0.000000e+00
# D_age_3 -0.80332424 0.0008757527 -917.29576 0.000000e+00
# D_age_4 -0.41906516 0.0012294722 -340.84965 0.000000e+00
# D_age_5 -0.29097802 0.0015627740 -186.19329 0.000000e+00
# D_age_6 -0.57299006 0.0021628918 -264.91850 0.000000e+00
# D_age_7 -0.36101594 0.0030016569 -120.27222 0.000000e+00
# D_age_8 -0.62706059 0.0046139466 -135.90547 0.000000e+00
# D_age_9 0.12160793 0.0061126021 19.89463 4.529830e-88
# D_age_10 -2.59708012 0.0245028290 -105.99103 0.000000e+00
# D_cohort_2 -0.02591843 0.0009037977 -28.67724 7.334840e-181
# D_cohort_3 0.18973130 0.0011301184 167.88621 0.000000e+00
# D_cohort_4 0.12354693 0.0010508785 117.56539 0.000000e+00
# D_cohort_5 -0.10114701 0.0010566534 -95.72392 0.000000e+00
# D_cohort_6 0.03594882 0.0010913718 32.93912 6.056847e-238
# D_cohort_7 -0.17175409 0.0011676536 -147.09336 0.000000e+00
# D_cohort_8 0.20671145 0.0012098255 170.86055 0.000000e+00
# D_cohort_9 0.04056617 0.0012325163 32.91329 1.418555e-237
# D_cohort_10 0.06876759 0.0015336998 44.83771 0.000000e+00
#########################
# Get deviance table.
# APC strongly rejected => overdispersion?
# AC (Chain-ladder) rejected against APC (inference invalid anyway)
# => one should be careful with distribution forecasts
apc.fit.table(data,"poisson.response")
#########################
# -2logL df.residual prob(>chi_sq) LR.vs.APC df.vs.APC prob(>chi_sq) aic
# APC 176030.0 28 0 NA NA NA 176841.7
# AP 305784.6 36 0 129754.6 8 0 306580.3
# AC 374155.2 36 0 198125.2 8 0 374950.9
# PC 553555.1 36 0 377525.0 8 0 554350.7
# Ad 486013.4 44 0 309983.4 16 0 486793.0
# Pd 710009.6 44 0 533979.6 16 0 710789.3
# Cd 780859.4 44 0 604829.4 16 0 781639.1
# A 575389.6 45 0 399359.6 17 0 576167.3
# P 9483688.1 45 0 9307658.0 17 0 9484465.7
# C 7969034.0 45 0 7793004.0 17 0 7969811.7
# t 898208.1 52 0 722178.1 24 0 898971.7
# tA 987389.4 53 0 811359.4 25 0 988151.1
# tP 9690623.4 53 0 9514593.4 25 0 9691385.1
# tC 8079187.6 53 0 7903157.6 25 0 8079949.3
# 1 10815443.5 54 0 10639413.5 26 0 10816203.2
#########################
# Fit geometric chain-ladder model
fit.ac <- apc.fit.model(data,"log.normal.response","AC")
fit.ac$coefficients.canonical
id.ac <- apc.identify(fit.ac)
id.ac$coefficients.dif
#########################
# Compare output with table 7.2 in
# Kuang D, Nielsen B, Nielsen JP (2015)
# Estimate Std. Error t value Pr(>|t|)
# level 13.0846325168 0.1322711 98.92285585 0.000000e+00
# D_age_2 -0.0721758004 0.1291053 -0.55904595 5.761304e-01
# D_age_3 -0.8180698189 0.1350216 -6.05880856 1.371335e-09
# D_age_4 -0.3945325384 0.1433094 -2.75301253 5.904964e-03
# D_age_5 -0.3354312554 0.1538274 -2.18056918 2.921530e-02
# D_age_6 -0.6322104515 0.1673396 -3.77800844 1.580875e-04
# D_age_7 -0.3020293471 0.1854134 -1.62895114 1.033234e-01
# D_age_8 -0.5225495852 0.2112982 -2.47304367 1.339678e-02
# D_age_9 0.0078494549 0.2531172 0.03101115 9.752607e-01
# D_age_10 -2.5601846890 0.3415805 -7.49511273 6.624141e-14
# D_cohort_2 -0.1025686798 0.1291053 -0.79445748 4.269292e-01
# D_cohort_3 0.0820931043 0.1350216 0.60799994 5.431875e-01
# D_cohort_4 0.3800465893 0.1433094 2.65193088 8.003292e-03
# D_cohort_5 -0.0920821506 0.1538274 -0.59860701 5.494350e-01
# D_cohort_6 -0.0530061052 0.1673396 -0.31675768 7.514275e-01
# D_cohort_7 -0.2053813051 0.1854134 -1.10769405 2.679940e-01
# D_cohort_8 0.2705853742 0.2112982 1.28058555 2.003393e-01
# D_cohort_9 -0.0009224552 0.2531172 -0.00364438 9.970922e-01
# D_cohort_10 0.0736954734 0.3415805 0.21574845 8.291838e-01
#########################
# Get deviance table.
# AC marginally rejected against APC
apc.fit.table(data,"log.normal.response")
#########################
# -2logL df.residual LR.vs.APC df.vs.APC prob(>chi_sq) aic
# APC -28.528 28 NA NA NA 27.472
# AP -3.998 36 24.530 8 0.002 36.002
# AC -9.686 36 18.842 8 0.016 30.314
# PC 31.722 36 60.250 8 0.000 71.722
# Ad 6.251 44 34.779 16 0.004 30.251
# Pd 41.338 44 69.866 16 0.000 65.338
# Cd 38.919 44 67.447 16 0.000 62.919
# A 12.765 45 41.292 17 0.001 34.765
# P 171.283 45 199.811 17 0.000 193.283
# C 162.451 45 190.979 17 0.000 184.451
# t 46.300 52 74.827 24 0.000 54.300
# tA 49.541 53 78.069 25 0.000 55.541
# tP 171.770 53 200.298 25 0.000 177.770
# tC 163.280 53 191.808 25 0.000 169.280
# 1 182.166 54 210.694 26 0.000 186.166