MunichChainLadder function

Munich-chain-ladder Model

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.

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 c("$k \\leq n+1-i; i=1,\\ldots,m,\n$", "$m\\geq n$")

• 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.

Returns

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.

Author(s)

Markus Gesmann markus.gesmann@gmail.com

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