Thanks to Marco De Virgilis.
Moved NEWS file into RMarkdown package vignette format.
Previously it was required that the row and column names of a triangle be convertible to numeric, although that “requirement” did not always cause a problem. For example, the following sets the rownames of GenIns to the beginning Date of the accident year.
<- GenIns
x rownames(x) <- paste0(2001:2010, "-01-01")
x
## dev
## origin 1 2 3 4 5 6 7 8 9 10
## 2001-01-01 357.8 1125 1735 2218 2746 3320 3466 3606 3834 3901
## 2002-01-01 352.1 1236 2170 3353 3799 4120 4648 4914 5339 NA
## 2003-01-01 290.5 1292 2219 3235 3986 4133 4629 4909 NA NA
## 2004-01-01 310.6 1419 2195 3757 4030 4382 4588 NA NA NA
## 2005-01-01 443.2 1136 2128 2898 3403 3873 NA NA NA NA
## 2006-01-01 396.1 1333 2181 2986 3692 NA NA NA NA NA
## 2007-01-01 440.8 1288 2420 3483 NA NA NA NA NA NA
## 2008-01-01 359.5 1421 2864 NA NA NA NA NA NA NA
## 2009-01-01 376.7 1363 NA NA NA NA NA NA NA NA
## 2010-01-01 344.0 NA NA NA NA NA NA NA NA NA
A plot with the lattice=TRUE
option, which previously would blow up, now displays with nice headings.
plot(x, lattice=TRUE)
It can often be useful to have “origin” values that are not necessarily convertible to numeric. For example, suppose you have a table of claim detail at various evaluation dates. Invariably, such a table will have a Date field holding the date of loss. It would be nice to be able to summarize that data by accident year “cuts”. It turns out there’s a builtin function in R that will get you most of the way there. It’s called ‘cut’.
Here we take the GenIns data in long format and generate 50 claims per accident period. We assign each claim a random date within the year. The incurred (or paid) “value” given is a random perturbation of one-fiftieth of GenInsLong$value.
We accumulate the detail into an accident year triangle using ChainLadder’s as.triangle
method. The summarized triangle displayed at the end is very similar to GenIns
, and has informative row labels.
<- GenInsLong
x # start off y with x's headings
<- x[0,]
y names(y)[1] <- "lossdate"
set.seed(1234)
= 50 # number of simulated claims per accident perior
n for (i in 1:nrow(x)) {
<- rbind(y,
y data.frame(
lossdate = as.Date(
as.numeric(as.Date(paste0(x[i, "accyear"]+2000, "-01-01"))) +
round(runif(n, 0, 364),0), origin = "1970-01-01"),
devyear = x[i, "devyear"],
incurred.claims = rnorm(n, mean = x[i, "incurred claims"] / n,
sd = x[i, "incurred claims"]/(10*n))
))
}# here's the magic cut
$ay <- cut(y$lossdate, breaks = "years")
y# this summarized triangle is very similar to GenIns
as.triangle(y, origin = "ay", dev = "devyear", value = "incurred.claims")
## devyear
## ay 1 2 3 4 5 6 7 8
## 2001-01-01 349741 1109368 1737850 2265706 2749056 3318464 3469142 3549578
## 2002-01-01 352821 1245621 2132200 3377061 3820987 4148933 4610189 4891852
## 2003-01-01 296548 1275881 2198221 3235844 3944931 4113276 4623159 4900318
## 2004-01-01 313669 1392038 2171462 3774168 4035879 4461897 4661352 NA
## 2005-01-01 443941 1138787 2190873 2905444 3371444 3849587 NA NA
## 2006-01-01 391527 1324732 2230006 3000719 3742811 NA NA NA
## 2007-01-01 446942 1292116 2416001 3404734 NA NA NA NA
## 2008-01-01 349330 1425022 2844242 NA NA NA NA NA
## 2009-01-01 369893 1368242 NA NA NA NA NA NA
## 2010-01-01 346493 NA NA NA NA NA NA NA
## devyear
## ay 9 10
## 2001-01-01 3769684 3980606
## 2002-01-01 5311927 NA
## 2003-01-01 NA NA
## 2004-01-01 NA NA
## 2005-01-01 NA NA
## 2006-01-01 NA NA
## 2007-01-01 NA NA
## 2008-01-01 NA NA
## 2009-01-01 NA NA
## 2010-01-01 NA NA
The user is encouraged to experiment with other cut’s – e.g., breaks = "quarters"
will generate accident quarter triangles.
A new function, as.LongTriangle
, will convert a triangle from “wide” (matrix) format to “long” (data.frame) format. This differs from ChainLadder’s as.data.frame.triangle method in that the rownames and colnames of Triangle are stored as factors. This feature can be particularly important when plotting a triangle because the order of the “origin” and “dev” values is important.
Additionally, the columns of the resulting data frame may be renamed from the default values (“origin”, “dev”, and “value”) using the “varnames” argument for “origin”/“dev” and the “value.name” argument for “value”.
In the following example, the GenIns
triangle in ChainLadder is converted to a data.frame
with non-default names:
<- as.LongTriangle(GenIns, varnames = c("accident year", "development age"),
GenLong value.name = "Incurred Loss")
head(GenLong)
## accident year development age Incurred Loss
## 1 1 1 357.8
## 2 2 1 352.1
## 3 3 1 290.5
## 4 4 1 310.6
## 5 5 1 443.2
## 6 6 1 396.1
In the following plot, the last accident year and the last development age are shown last, rather than second as they would have been if displayed alphabetically (ggplot’s default for character data):
library(ggplot2)
ggplot(GenLong, aes(x=`development age`, y = `Incurred Loss`,
group = `accident year`, color = `accident year`)) +
geom_line()
Previously, when an “exposure” attribute was assigned to a triangle for use with glmReserve
, it was assumed/expected that the user would supply the values in the same order as the accident years. Then, behind the scenes, glmReserve would use an arithmetic formula to match the exposure with the appropriate accident year using the numeric “origin” values after the triangle had been converted to long format.
glmReserve
now allows for “exposure” to have “names” that coincide with the rownames of the triangle, which are used to match to origin in long format. Here is an example, newly found in ?glmReserve
.
<- GenIns
GenIns2 rownames(GenIns2) <- paste0(2001:2010, "-01-01")
<- (7 + 1:10 * 0.4) * 10
expos names(expos) <- rownames(GenIns2)
attr(GenIns2, "exposure") <- expos
glmReserve(GenIns2)
## Latest Dev.To.Date Ultimate IBNR S.E CV
## 2002-01-01 5339 0.98252 5434 95 110.1 1.1589
## 2003-01-01 4909 0.91263 5379 470 216.0 0.4597
## 2004-01-01 4588 0.86599 5298 710 260.9 0.3674
## 2005-01-01 3873 0.79725 4858 985 303.6 0.3082
## 2006-01-01 3692 0.72235 5111 1419 375.0 0.2643
## 2007-01-01 3483 0.61527 5661 2178 495.4 0.2274
## 2008-01-01 2864 0.42221 6784 3920 790.0 0.2015
## 2009-01-01 1363 0.24162 5642 4279 1046.5 0.2446
## 2010-01-01 344 0.06922 4970 4626 1980.1 0.4280
## total 30457 0.61982 49138 18681 2945.7 0.1577
The glmReserve
function now supports the negative binomial GLM, a more natural way to model over-dispersion in count data. The model is fitted through the glm.nb
function from the MASS
package.
To fit the negative binomial GLM to the loss triangle, simply set nb = TRUE
in calling the glmReserve function:
<- glmReserve(GenIns, nb = TRUE)) (fit6
## Latest Dev.To.Date Ultimate IBNR S.E CV
## 2 5339 0.98288 5432 93 39.61 0.4260
## 3 4909 0.91655 5356 447 133.66 0.2990
## 4 4588 0.88197 5202 614 148.48 0.2418
## 5 3873 0.79594 4866 993 211.05 0.2125
## 6 3692 0.71771 5144 1452 290.03 0.1997
## 7 3483 0.61440 5669 2186 433.05 0.1981
## 8 2864 0.43837 6534 3670 772.92 0.2106
## 9 1363 0.24826 5491 4128 967.76 0.2344
## 10 344 0.07076 4862 4518 1380.14 0.3055
## total 30457 0.62724 48557 18100 2232.92 0.1234
New files in the /inst/unittests/
folder can be used for future enhancements
Contributors of new contributions to those R files are encouraged to utilize those runit scripts for testing, and, of course, add other runit scripts as warrantted.
By default, R’s lm
method generates a warning when it detects an “essentially perfect fit”. This can happen when one column of a triangle is identical to the previous column; i.e., when all link ratios in a column are the same. In the example below, the second column is a fixed constant, 1.05, times the first column. ChainLadder previously issued the lm warning below.
x <- matrix(byrow = TRUE, nrow = 4, ncol = 4,
dimnames = list(origin = LETTERS[1:4], dev = 1:4),
data = c(
100, 105, 106, 106.5,
200, 210, 211, NA,
300, 315, NA, NA,
400, NA, NA, NA)
)
mcl <- MackChainLadder(x, est.sigma = "Mack")
Warning messages:
1: In summary.lm(x) : essentially perfect fit: summary may be unreliable
2: In summary.lm(x) : essentially perfect fit: summary may be unreliable
3: In summary.lm(x) : essentially perfect fit: summary may be unreliable
which may have raised a concern with the user when none was warranted.
Now ChainLadder issues an “informational warning”:
<- MackChainLadder(x, est.sigma = "Mack") mcl
## Warning in Mack.S.E(CL[["Models"]], FullTriangle, est.sigma = est.sigma, : Information: essentially no variation in development data for period(s):
## '1-2'
Fixed tail extrapolation in Vignette. (Thanks to Mark Lee.)
Added back functionality to estimate the index parameter for the compound Poisson model in ‘glmReserve’ (now depends on package cplm). This works for both ‘formula’ and ‘bootstrap’.
Added methods ‘resid’ and plot for class ‘glmReserve’ (now depends on ggplot2)
New function PaidIncurredChain by Fabio Concina, based on the 2010 Merz & Wuthrich paper Paid-incurred chain claims reserving method
plot.MackChainLadder and plot.BootChainLadder gained new argument
‘which’, allowing users to specify which sub-plot to display. Thanks to Christophe Dutang for this suggestion.
Updated NAMESPACE file to comply with new R CMD checks in R-3.3.0
Removed package dependencies on grDevices and Hmisc
Expanded package vignette with new paragraph on importing spreadsheet data, a new section “Paid-Incurred Chain Model” and an added example for a full claims development picture in the “One Year Claims Development Result” section.
New generic function CDR to estimate the one year claims development result. S3 methods for the Mack and bootstrap model have been added already:
New function tweedieReserve to estimate reserves in a GLM framework, including the one year claims development result.
Package vignette has new chapter ‘One Year Claims Development Result’.
New example data MW2008 and MW2014 form the Merz & Wuthrich (2008, 2014) papers
Source code development moved from Google Code to GitHub: https://github.com/mages/ChainLadder
as.data.frame.triangle now gives warning message when dev. period is a character
Alessandro Carrato, Giuseppe Crupi and Mario Wuthrich have been added as authors, thanks to their major contribution to code and documentation
Christophe Dutang, Arnaud Lacoume and Arthur Charpentier have been added as contributors, thanks to their feedback, guidance and code contribution
A new function, CLFMdelta, finds the value of delta such that the model coefficients resulting from the ‘chainladder’ function with that value for argument delta are consistent with an input vector of ‘selected’ age-to-age factors, subject to restrictions on the ‘selected’ factors relative to the input ‘Triangle’. See the paper “A Family of Chain-Ladder Factor Models for Selected Link Ratios” by Bardis, Majidi, Murphy, Variance Journal
A new ‘coef’ method returns the age-to-age factor coefficients of the regression models estimated by the ‘chainladder’ function.
Exports a function “LRfunction” that calculates a Triangle’s link ratio function and can be used to plot the space of “reasonable link ratio selections” per the CLFM paper.
ClarkLDF and ClarkCapeCod functions: additional functionality
A ‘vcov’ method now exists to produce the covariance matrix of the estimated parameters using the approach in Clark’s paper
Additional values (in lists) returned by Clark’s methods:
Fine-tuning of maximum likelihood numerical algorithm’s control parameters
If the solution is found at the boundary of the parameter region, it is conceivable that a “more optimal” solution might exist if the boundary constraints were not as conservative, so a warning is given
The parameters returned by the methods were the scaled versions; they now at their original scales.
The loss development factor (LDF) being returned by ClarkCapeCod was not documented
New implementation of the methods in David Clark’s “LDF Curve Fitting” paper in the 2003 Forum by Daniel Murphy.
‘MackChainLadder’ has new argument ‘alpha’ as an additional weighting parameter. As a result, the argument ‘weights’ is now just that, weights should be between 0 and 1. The argument ‘alpha’ describes the different chain ladder age-to-age factors: The default for alpha for all development periods is 1. See Mack’s 1999 paper: alpha=1 gives the historical chain ladder age-to-age factors, alpha=0 gives the straight average of the observed individual development factors and alpha=2 is the result of an ordinary regression with intercept 0.
Basic ‘chainladder’ function now available using linear models. See ?chainladder for more information.
More examples for ‘MackChainLadder’ demonstrate how to apply the MackChainLadder over several triangles in ‘one-line’.
‘as.data.frame.triangle’ has new argument ‘lob’ (e.g. line of business) which allows to set an additional label column in the data frame output.
‘MackChainLadder’: Latest position of incomplete triangles were in some cases not returned correctly. Thanks to Ben Escoto for reporting and providing a patch.
‘MackChainLadder’:
New triangle class with S3 methods for plot, print and conversion from triangles to data.frames and vis versa
New utility functions ‘incr2cum’ and ‘cum2incr’ to convert incremental triangles into cumulative triangles and vis versa. Thanks to Chritophe Dutang.
New logical argument lattice for plot.MackChainLadder (and plot.triangle), which allows to plot developments by origin period in separate panels.