### 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 use (mxn)-development triangles with m

### 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 the number of bootstrap replicates

### Note

The implementation of BootChainLadder follows closely the discussion of the bootstrap model in section 8 and appendix 3 of the paper by England and Verrall (2002).

### 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 summary.BootChainLadder, plot.BootChainLadder displaying results and finally CDR.BootChainLadder for the one year claims development result.

### Examples

# See also the example in section 8 of England & Verrall (2002) on page 55.

B
plot(B)
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)