Standard deviation of the claims development result after one year for the distribution-free chain-ladder model (Mack) and Bootstrap model.
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otput of either
vector of development periods or
only applicable for
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)
data.frame with various IBNR/reserves and one-year statistics of the
claims development result.
Tail factors are currently not supported.
Mario Wüthrich and Markus Gesmann
with contributions from Arthur Charpentier and Arnaud Lacoume
CDR.MackChainLadder and Giuseppe Crupi and
Markus Gesmann for
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. http://ssrn.com/abstract=2524352. 2014
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# 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)