BootChainLadder function

Bootstrap-Chain-Ladder Model

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"), seed = NULL)

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<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" (over-dispersed Poisson), can be abbreviated

• seed: optional seed for the random generator

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.

Returns

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

References

England, PD and Verrall, RJ. Stochastic Claims Reserving in GeneralInsurance (with discussion), British Actuarial Journal 8, III. 2002

Barnett and Zehnwirth. The need for diagnostic assessment of bootstrappredictive models, Insureware technical report. 2007

Author(s)

Markus Gesmann, markus.gesmann@gmail.com

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).

See Also

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 <- 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)