BootChainLadder {ChainLadder}R Documentation

Bootstrap-Chain-Ladder Model

Description

The BootChainLadder procedure provides a predictive distribution of reserves or IBNRs for a cumulative claims development triangle.

Usage

BootChainLadder(Triangle, R = 999, process.distr=c("gamma", "od.pois"))

Arguments

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

Details

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.

Value

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

Note

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.

Author(s)

Markus Gesmann, markus.gesmann@gmail.com

References

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

See also summary.BootChainLadder, MackChainLadder

Examples

# 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)



[Package ChainLadder version 0.1.2-11 Index]