ChainLadder (version 0.1.6)

MunichChainLadder: 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)

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 MackChain

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 MackCha

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.

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

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