ChainLadder: CDR – R documentation

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CDR

One year claims development result

Description

Standard deviation of the claims development result after one year for the distribution-free chain-ladder model (Mack) and Bootstrap model.

Usage

CDR(x, ...)
## S3 method for class 'MackChainLadder'
CDR(x, dev=1, ...)
## S3 method for class 'BootChainLadder'
CDR(x, probs=c(0.75, 0.95), ...)
## Default S3 method:
CDR(x, ...)

Arguments

`x`	otput of either `MackChainLadder` or `BootChainLadder`
`dev`	vector of development periods or `"all"`. Currently only applicable for `MackChainLadder` output. Defines the years for which the run off claims development result should be returned.
`probs`	only applicable for `BootChainLadder` output. Define quantiles to be returned.
`...`	other arguments

Details

Merz & Wüthrich (2008) derived analytic formulae for the mean square error of prediction of the claims development result for the Mack chain-ladder model after one year assuming:

The opening reserves were set using the pure chain-ladder model (no tail)
Claims develop in the year according to the assumptions underlying Mack's model
Reserves are set after one year using the pure chain-ladder model (no tail)

Value

A data.frame with various IBNR/reserves and one-year statistics of the claims development result.

Note

Tail factors are currently not supported.

Author(s)

Mario Wüthrich and Markus Gesmann with contributions from Arthur Charpentier and Arnaud Lacoume for CDR.MackChainLadder and Giuseppe Crupi and Markus Gesmann for CDR.BootChainLadder.

References

Michael Merz, Mario V. Wüthrich. Modelling the claims development result for solvency purposes. Casualty Actuarial Society E-Forum, Fall 2008.

Michael Merz, Mario V. Wüthrich. Claims Run-Off Uncertainty: The Full Picture. Swiss Finance Institute Research Paper No. 14-69. https://www.ssrn.com/abstract=2524352. 2014

Examples

# Example from the 2008 Merz, Wuthrich paper mentioned above
MW2008
M <- MackChainLadder(MW2008, est.sigma="Mack")
plot(M)
CDR(M)
# Return all run-off result developments
CDR(M, dev="all")

# Example from the 2014 Merz, Wuthrich paper mentioned above
MW2014
W <- MackChainLadder(MW2014, est.sigma="Mack")
plot(W)
CDR(W)

# Example with the BootChainLadder function, assuming overdispered Poisson model
B <- BootChainLadder(MW2008, process.distr=c("od.pois"))
B
CDR(B)

ChainLadder

Statistical Methods and Models for Claims Reserving in General Insurance

v0.2.12

GPL (>= 2)

Authors

Markus Gesmann [aut, cre], Daniel Murphy [aut], Yanwei (Wayne) Zhang [aut], Alessandro Carrato [aut], Giuseppe Crupi [ctb], Christophe Dutang [ctb], Arnaud Lacoume [ctb], Arthur Charpentier [ctb], Mario Wuthrich [aut], Fabio Concina [aut], Eric Dal Moro [aut], Yuriy Krvavych [ctb], Vincent Goulet [ctb], Marco De Virgilis [ctb]

Initial release

2021-01-05

CDR