ChainLadder (version 0.1.1-1)

MunichChainLadder: Munich-Chain-Ladder Model

Description

Munich-Chain-Ladder model to forecast IBNR claims based on a cumulative paid and incurred claims triangle. The Munich-Chain-Ladder model assumes that the Mack-model is applicable to the paid and incurred claims triangle, see MackChainLadder.

Usage

MunichChainLadder(Paid, Incurred)
## S3 method for class 'MunichChainLadder':
print(x, \dots)
## S3 method for class 'MunichChainLadder':
plot(x,  mfrow=c(2,2), title=NULL, \dots)
## S3 method for class 'MunichChainLadder':
summary(object, \dots)

Arguments

Paid

cumulative paid claims triangle. A quadratic (nxn)-matrix $P_{ik}$ which is filled for $k \leq n+1-i, i=1,\ldots,n$

Incurred

cumulative incurred claims triangle. A quadratic (nxn)-matrix $I_{ik}$ which is filled for $k \leq n+1-i, i=1,\ldots,n$

x, object

an object of class "MunichChainLadder"

mfrow

see par

title

see title

...

not in use

Value

• MunichChainLadder returns a list with the following values
• 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
• SCLPaid
  standard-chain-ladder forecasted full triangle on paid data
• SCLIncurred
  standard-chain-ladder forecasted full triangle on Incurred data
• PaidResiduals
  paid residuals
• IncurredResiduals
  incurred residuals
• QResiduals
  paid/incurred residuals
• QinverseResiduals
  incurred/paid residuals
• lambdaP
  dependency coefficient between paid chain ladder ratios and incurred/paid ratios
• lambdaI
  dependency coefficient between incurred chain ladder ratios and paid/incurred ratios

References

Gerhard Quarg and Thomas Mack. Munich Chain Ladder. Blatter DGVFM 26, Munich, 2004.

See Also

See also MackChainLadder

Examples

# Munich Chain Ladder
Paid <- t(matrix(c(
  576, 1804, 1970, 2024, 2074, 2102, 2131,
  866, 1948, 2162, 2232, 2284, 2348,   NA,
 1412, 3758, 4252, 4416, 4494,   NA,   NA,
 2286, 5292, 5724, 5850,   NA,   NA,   NA,
 1868, 3778, 4648,   NA,   NA,   NA,   NA,
 1442, 4010,   NA,   NA,   NA,   NA,   NA,
 2044,   NA,   NA,   NA,   NA,   NA,   NA
 ), ncol=7))
 	
Incurred <- t(matrix(c( 
  978, 2104, 2134, 2144, 2174, 2182, 2174,
 1844, 2552, 2466, 2480, 2508, 2454,   NA,
 2904, 4354, 4698, 4600, 4644,   NA,   NA,
 3502, 5958, 6070, 6142,   NA,   NA,   NA,
 2812, 4882, 4852,   NA,   NA,   NA,   NA,
 2642, 4406,   NA,   NA,   NA,   NA,   NA,
 5022,   NA,   NA,   NA,   NA,   NA,   NA
 ), ncol=7))

MCL = MunichChainLadder(Paid, Incurred)
MCL
plot(MCL)