MunichChainLadder: Munich-chain-ladder Model

In ChainLadder: Statistical Methods and Models for Claims Reserving in General Insurance

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

ChainLadder documentation built on Sept. 11, 2024, 8:35 p.m.