MunichChainLadder {ChainLadder} | R Documentation |
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
.
MunichChainLadder(Paid, Incurred, est.sigmaP = "log-linear", est.sigmaI = "log-linear", tailP=FALSE, tailI=FALSE)
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.sigmaI |
defines how sigma_{n-1} for the Incurred triangle
is estimated, see |
tailP |
defines how the tail of the |
tailI |
defines how the tail of the |
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 |
Markus Gesmann markus.gesmann@gmail.com
Gerhard Quarg and Thomas Mack. Munich Chain Ladder. Blatter DGVFM 26, Munich, 2004.
See also
summary.MunichChainLadder
,
plot.MunichChainLadder
,
MackChainLadder
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