# BootChainLadder: Bootstrap-Chain-Ladder Model In ChainLadder: Statistical Methods and Models for Claims Reserving in General Insurance

## Description

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

## Usage

 `1` ```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 ≤ n+1-i; i=1,…,m; m≥ 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.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```# 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) ## One year claims development result CDR(A) ```