MunichChainLadder {ChainLadder}

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, weights=1)

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 \leq n+1-i; i=1,\ldots,m; m\geq 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 \leq n+1-i; i=1,\ldots,m, m\geq 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.

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 age-to-age 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

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 [e-mail]

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