MunichChainLadder {ChainLadder}R Documentation

Munich-chain-ladder Model

Description

The Munich-chain-ladder model forecasts ultimate claims based on a cumulative paid and incurred claims triangle. The model assumes that the Mack-chain-ladder model is applicable to the paid and incurred claims triangle, see MackChainLadder.

Usage

MunichChainLadder(Paid, Incurred, 
                  est.sigmaP = "log-linear", est.sigmaI = "log-linear", 
                  tailP=FALSE, tailI=FALSE)

Arguments

Paid cumulative paid claims triangle. Assume columns are the development period, use transpose otherwise. A (mxn)-matrix P_{ik} which is filled for k <=q n+1-i; i=1,...,m; m>=q n
Incurred cumulative incurred claims triangle. Assume columns are the development period, use transpose otherwise. A (mxn)-matrix I_{ik} which is filled for k <=q n+1-i; i=1,...,m, m>=q n
est.sigmaP defines how sigma_{n-1} for the Paid triangle is estimated, see est.sigma in MackChainLadder for more details, as est.sigmaP gets passed on to MackChainLadder
est.sigmaI defines how sigma_{n-1} for the Incurred triangle is estimated, see est.sigma in MackChainLadder for more details, as est.sigmaI is passed on to MackChainLadder
tailP defines how the tail of the Paid triangle is estimated and is passed on to MackChainLadder, see tail just there.
tailI defines how the tail of the Incurred triangle is estimated and is passed on to MackChainLadder, see tail just there.

Value

MunichChainLadder returns a list with the following elements

call matched call
Paid input paid triangle
Incurred input incurred triangle
MCLPaid Munich-chain-ladder forecasted full triangle on paid data
MCLIncurred Munich-chain-ladder forecasted full triangle on incurred data
MackPaid Mack-chain-ladder output of the paid triangle
MackIncurred Mack-chain-ladder output of the incurred triangle
PaidResiduals paid residuals
IncurredResiduals incurred residuals
QResiduals paid/incurred residuals
QinverseResiduals incurred/paid residuals
lambdaP dependency coefficient between paid chain ladder age-to-age factors and incurred/paid age-to-age factors
lambdaI dependency coefficient between incurred chain ladder ratios and paid/incurred ratios
qinverse.f chain-ladder-link age-to-age factors of the incurred/paid triangle
rhoP.sigma estimated conditional deviation around the paid/incurred age-to-age factors
q.f chain-ladder age-to-age factors of the paid/incurred triangle
rhoI.sigma estimated conditional deviation around the incurred/paid age-to-age factors

Author(s)

Markus Gesmann markus.gesmann@gmail.com

References

Gerhard Quarg and Thomas Mack. Munich Chain Ladder. Blatter DGVFM 26, Munich, 2004.

See Also

See also summary.MunichChainLadder, plot.MunichChainLadder , MackChainLadder

Examples


MCLpaid
MCLincurred
op <- par(mfrow=c(1,2))
plot(MCLpaid)
plot(MCLincurred)
par(op)

# Following the example in Quarg's (2004) paper:
MCL <- MunichChainLadder(MCLpaid, MCLincurred, est.sigmaP=0.1, est.sigmaI=0.1)
MCL
plot(MCL)
# You can access the standard chain ladder (Mack) output via
MCL$MackPaid
MCL$MackIncurred

# Input triangles section 3.3.1
MCL$Paid
MCL$Incurred
# Parameters from section 3.3.2
# Standard chain ladder age-to-age factors
MCL$MackPaid$f
MCL$MackIncurred$f
MCL$MackPaid$sigma
MCL$MackIncurred$sigma
# Check Mack's assumptions graphically
plot(MCL$MackPaid)
plot(MCL$MackIncurred)

MCL$q.f
MCL$rhoP.sigma
MCL$rhoI.sigma

MCL$PaidResiduals
MCL$IncurredResiduals

MCL$QinverseResiduals
MCL$QResiduals

MCL$lambdaP
MCL$lambdaI
# Section 3.3.3 Results
MCL$MCLPaid
MCL$MCLIncurred


[Package ChainLadder version 0.1.2-13 Index]