ChainLadder (version 0.1.7)

BootChainLadder: 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. Assume columns are the development period, use transpose otherwise. A (mxn)-matrix $C_{ik}$ which is filled for $k \le n+1-i; i=1,\ldots,m; m\ge n$. See qpaid for how to

R

the number of bootstrap replicates.

process.distr

character string indicating which process distribution to be assumed. One of "gamma" (default), or "od.pois" (over-dispersed Poisson), can be abbreviated

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
  the number of bootstrap replicates

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.

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, plot.BootChainLadder

Examples

# See also the example in section 8 of England & Verrall (2002) 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 also the ABC example in  Barnett and Zehnwirth (2007) 
A <- BootChainLadder(ABC, R=999, process.distr="gamma")
A
plot(A, log=TRUE)