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
1 2 3 
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+1i; 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+1i; i=1,…,m, m≥q n 
est.sigmaP 
defines how sigma_{n1} for the Paid triangle
is estimated, see 
est.sigmaI 
defines how sigma_{n1} for the Incurred triangle
is estimated, see 
tailP 
defines how the tail of the 
tailI 
defines how the tail of the 
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 chain ladder agetoage factors and incurred/paid agetoage factors 
lambdaI 
dependency coefficient between incurred chain ladder 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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43  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 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

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