MunichChainLadder {ChainLadder} | R Documentation |
The Munich-Chain-Ladder model forecasts IBNR claims based on a cumulative
paid and incurred claims triangle.
The Munich-Chain-Ladder model assumes that the Mack-model is applicable
to the paid and incurred claims triangle, see MackChainLadder
.
MunichChainLadder(Paid, Incurred, est.sigmaP = "log-linear", est.sigmaI = "log-linear", tailP=FALSE, tailI=FALSE)
Paid |
cumulative paid claims triangle. 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. 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. |
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 ratios and incurred/paid ratios |
lambdaI |
dependency coefficient between incurred chain ladder ratios and paid/incurred ratios |
qinverse.f |
chain-ladder-link-ratio of the incurred/paid triangle |
rhoP.sigma |
estimation of the conditional deviation around the paid/incurred ratios |
q.f |
chain-ladder-link-ratio of the paid/incurred triangle |
rhoI.sigma |
estimation of the conditional deviation around the incurred/paid ratios |
Markus Gesmann markus.gesmann@gmail.com
Gerhard Quarg and Thomas Mack. Munich Chain Ladder. Blatter DGVFM 26, Munich, 2004.
See also MackChainLadder
,
summary.MunichChainLadder
,
plot.MunichChainLadder
MCLpaid MCLincurred M <- MunichChainLadder(MCLpaid, MCLincurred) M plot(M) # You can access the standard chain ladder (Mack) output via M$MackPaid M$MackIncurred # Following the example output in Quarg's paper: MCL <- MunichChainLadder(MCLpaid, MCLincurred, est.sigmaP=0.1, est.sigmaI=0.1) # Input triangles section 3.3.1 MCL$Paid MCL$Incurred # Parameters from section 3.3.2 # Standard chain ladder 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