BootChainLadder {ChainLadder} | R Documentation |
The BootChainLadder
procedure provides a predictive
distribution of reserves or IBNRs for a cumulative claims development triangle.
BootChainLadder(Triangle, R = 999, process.distr=c("gamma", "od.pois"))
Triangle |
cumulative claims triangle. A (mxn)-matrix C_{ik}
which is filled for k <= n+1-i; i=1,...,m; m>= n , see
qpaid for how to use (mxn)-development triangles with
m<n, say higher development period frequency (e.g quarterly) than
origin period frequency (e.g accident years). |
R |
the number of bootstrap replicates. |
process.distr |
character string indicating which process distribution to be assumed. One of "gamma" (default), or "od.pois" (overdispersed Poisson), can be abbreviated |
The BootChainLadder
function uses a two-stage
bootstrapping/simulation approach. In the first stage an ordinary
chain-ladder methods is applied to the cumulative claims triangle.
From this we calculate the scaled Pearson residuals which we bootstrap
R times to forecast future incremental claims payments via the
standard chain-ladder method.
In the second stage we simulate the process error with the bootstrap
value as the mean and using the process distribution assumed.
The set of reserves obtained in this way forms the predictive distribution,
from which summary statistics such as mean, prediction error or
quantiles can be derived.
BootChainLadder gives a list with the following elements back:
call |
matched call |
Triangle |
input triangle |
f |
chain-ladder factors |
simClaims |
array of dimension c(m,n,R) with the simulated claims |
IBNR.ByOrigin |
array of dimension c(m,1,R) with the modeled
IBNRs by origin period |
IBNR.Triangles |
array of dimension c(m,n,R) with the modeled
IBNR development triangles |
IBNR.Totals |
vector of R samples of the total IBNRs |
ChainLadder.Residuals |
adjusted Pearson chain-ladder residuals |
process.distr |
assumed process distribution |
R |
number of bootstraps |
The implimentation of BootChainLadder
follows closely the
discussion of the bootstrap model in section 8 and appendix 3 of the
paper by England and Verall.
Markus Gesmann, markus.gesmann@gmail.com
England, PD and Verrall, RJ. Stochastic Claims Reserving in General Insurance (with discussion), British Actuarial Journal 8, III. 2002
Barnett and Zehnwirth. The need for diagnostic assessment of bootstrap predictive models, Insureware technical report. 2007
See also summary.BootChainLadder
, MackChainLadder
# See as well the example in section 8 of England & Verrall's paper on page 55. B <- BootChainLadder(RAA, R=999, process.distr="gamma") B plot(B) # Compare to MackChainLadder MackChainLadder(RAA) quantile(B, c(0.75,0.95,0.99, 0.995)) # fit a distribution to the IBNR library(MASS) plot(ecdf(B$IBNR.Totals)) # fit a log-normal distribution fit <- fitdistr(B$IBNR.Totals[B$IBNR.Totals>0], "lognormal") fit curve(plnorm(x,fit$estimate["meanlog"], fit$estimate["sdlog"]), col="red", add=TRUE) # See as well the ABC example in the Barnett and Zehnwirth paper A <- BootChainLadder(ABC, R=999, process.distr="gamma") A plot(A, log=TRUE)