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"), seed = NULL)
```

### Arguments

`Triangle` |
cumulative claims triangle. Assume columns are the development
period, use transpose otherwise. A (mxn)-matrix |

`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.

### Value

BootChainLadder gives a list with the following elements back:

`call` |
matched call |

`Triangle` |
input triangle |

`f` |
chain-ladder factors |

`simClaims` |
array of dimension |

`IBNR.ByOrigin` |
array of dimension |

`IBNR.Triangles` |
array of dimension |

`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

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)
```

*ChainLadder*version 0.2.18 Index]