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

Examples

Run this code

# 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)

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