MunichChainLadder {ChainLadder}  R Documentation 
Munichchainladder Model
Description
The Munichchainladder model forecasts ultimate claims based on a cumulative
paid and incurred claims triangle.
The model assumes that the Mackchainladder model is applicable
to the paid and incurred claims triangle, see MackChainLadder
.
Usage
MunichChainLadder(Paid, Incurred,
est.sigmaP = "loglinear", est.sigmaI = "loglinear",
tailP=FALSE, tailI=FALSE, weights=1)
Arguments
Paid 
cumulative paid claims triangle. Assume columns are the development
period, use transpose otherwise. A (mxn)matrix 
Incurred 
cumulative incurred claims triangle. Assume columns are the development
period, use transpose otherwise. A (mxn)matrix

est.sigmaP 
defines how 
est.sigmaI 
defines how 
tailP 
defines how the tail of the 
tailI 
defines how the tail of the 
weights 
weights. Default: 1, which sets the weights for all triangle entries to 1. Otherwise specify weights as a matrix of the same dimension as Triangle with all weight entries in [0; 1]. Hence, any entry set to 0 or NA eliminates that agetoage factor from inclusion in the model. See also 'Details' in MackChainladder function. The weight matrix is the same for Paid and Incurred. 
Value
MunichChainLadder returns a list with the following elements
call 
matched call 
Paid 
input paid triangle 
Incurred 
input incurred triangle 
MCLPaid 
Munichchainladder forecasted full triangle on paid data 
MCLIncurred 
Munichchainladder forecasted full triangle on incurred data 
MackPaid 
Mackchainladder output of the paid triangle 
MackIncurred 
Mackchainladder output of the incurred triangle 
PaidResiduals 
paid residuals 
IncurredResiduals 
incurred residuals 
QResiduals 
paid/incurred residuals 
QinverseResiduals 
incurred/paid residuals 
lambdaP 
dependency coefficient between paid chainladder agetoage factors and incurred/paid agetoage factors 
lambdaI 
dependency coefficient between incurred chainladder ratios and paid/incurred ratios 
qinverse.f 
chainladderlink agetoage factors of the incurred/paid triangle 
rhoP.sigma 
estimated conditional deviation around the paid/incurred agetoage factors 
q.f 
chainladder agetoage factors of the paid/incurred triangle 
rhoI.sigma 
estimated conditional deviation around the incurred/paid agetoage 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 chainladder (Mack) output via
MCL$MackPaid
MCL$MackIncurred
# Input triangles section 3.3.1
MCL$Paid
MCL$Incurred
# Parameters from section 3.3.2
# Standard chainladder agetoage 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