ChainLadder (version 0.2.15)

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 MackChainLadder
CDR(x, dev=1, ...)
# S3 method for BootChainLadder
CDR(x, probs=c(0.75, 0.95), ...)
# S3 method for default
CDR(x, ...)

Value

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

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

Author

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.

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)

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

See Also

See also MackChainLadder and BootChainLadder

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)