bdcl.estimation: Parameter estimation - DCL model using the BDCL method
In DCL: Claims Reserving under the Double Chain Ladder Model

bdcl.estimation

R Documentation

Parameter estimation - DCL model using the BDCL method

Description

Estimate the parameters in the Double Chain Ladder model (delay parameters, severity mean and variance) using the Double Chain Ladder method with a Bornhuetter-Ferguson adjustment. The Bornhuetter-Ferguson tecnhique is applied to stabilise the underwriting inflation parameters using incurred data

Usage

bdcl.estimation( Xtriangle , Ntriangle , Itriangle , adj = 1 , 
   Tables=TRUE , num.dec=4 , n.cal=NA , Fj.X=NA , Fj.N=NA , Fj.I=NA)

Arguments

`Xtriangle`	The paid run-off triangle: incremental aggregated payments. It should be a matrix with incremental aggregated payments located in the upper triangle and the lower triangle consisting in missing or zero values.
`Ntriangle`	The counts data triangle: incremental number of reported claims. It should be a matrix with the observed counts located in the upper triangle and the lower triangle consisting in missing or zero values. It should has the same dimension as `Xtriangle` (both in the same aggregation level (quarters, years,etc.))
`Itriangle`	The incurred triangle. It should be a matrix with incurred data located in the upper triangle. It is an incremental run-off triangle with the same dimension as `Xtriangle` (both in the same aggregation level (quarters, years,etc.))
`adj`	Method to adjust the estimated delay parameters for the distributional model. It should be 1 (default value) or 2. See more in details below.
`Tables`	Logical. If TRUE (default) it is showed a table with the estimated parameters.
`num.dec`	Number of decimal places used to report numbers in the tables (if Tables=TRUE).
`n.cal`	Integer specifying the number of most recent calendars which will be used to calculate the development factors. By default `n.cal=NA` and all the observed calendars are used (classical chain ladder).
`Fj.X`	Optional vector with lentgth m-1 (m being the dimension of the triangles) with the development factors to calculate the chain ladder estimates from `Xtriangle`. See more details in `clm`.
`Fj.N`	Optional vector with lentgth m-1 with the development factors to calculate the chain ladder estimates from `Ntriangle`.
`Fj.I`	Optional vector with lentgth m-1 with the development factors to calculate the chain ladder estimates from `Itriangle`.

Details

Two model are estimated in the double chain ladder framework as with the dcl.estimation function. In this case the inflation parameter (inflat) is estimated from the incurred triangle (see BF adjustment in the description of the BDCL method in Martinez-Miranda, Nielsen and Verrall 2013). The predicted reserve using these estimates is different from the incurred reserve. If you want to reproduce exactly the incurred reserve (by splitting it into its RBNS and IBNR components) then use the function idcl.estimation.

Value

`pi.delay`	General delay parameters
`mu`	Mean severity factor
`inflat`	Underwriting severity inflation (BDCL inflation)
`inflat.DCL`	Underwriting severity inflation (DCL inflation)
`pj`	Delay probabilities (under a Multinomial assumption)
`mu.adj`	Adjusted mean factor corresponding to the `pj` parameters
`sigma2`	Variance severity factor
`phi`	Overdispersion parameter used to derive the estimate `sigma2`
`Ey`	Severity mean for each underwriting period
`Vy`	Severity variance for each underwriting period
`adj`	Type of adjusted used to derive the `pj` probabilities
`alpha.N`	Underwriting chain ladder parameter in the (OD)-Poisson model. Counts triangle (Ntriangle)
`beta.N`	Underwriting chain ladder parameter in the (OD)-Poisson model. Counts triangle (Ntriangle)
`Nhat`	The chain ladder preditions (counts triangle). It is a matrix having the chain ladder predictions in the future (lower triangle) and the fitted values in the past (upper triangle).
`alpha.X`	Underwriting chain ladder parameter in the (OD)-Poisson model. Paid triangle (Xtriangle)
`beta.X`	Underwriting chain ladder parameter in the (OD)-Poisson model. Paid triangle (Xtriangle)
`Xhat`	The chain ladder preditions (paid triangle). It is a matrix having the chain ladder predictions in the future (lower triangle) and the fitted values in the past (upper triangle).
`alpha.I`	Underwriting chain ladder parameter in the (OD)-Poisson model. Incurred triangle (Itriangle)
`beta.I`	Underwriting chain ladder parameter in the (OD)-Poisson model. Incurred triangle (Itriangle)

Author(s)

M.D. Martinez-Miranda, J.P. Nielsen and R. Verrall

References

Martinez-Miranda, M.D., Nielsen, J.P. and Verrall, R. (2012) Double Chain Ladder. Astin Bulletin, 42/1, 59-76.

Martinez-Miranda, M.D., Nielsen, J.P. and Verrall, R. (2013) Double Chain Ladder and Bornhuetter-Ferguson. North Americal Actuarial Journal.

Examples

# Reproducing the data analysis in the paper by Martinez-Miranda, Nielsen and Verrall (2013) 
data(NtriangleBDCL)
data(XtriangleBDCL)
data(ItriangleBDCL)

my.bdcl.par<-bdcl.estimation(XtriangleBDCL,NtriangleBDCL,ItriangleBDCL)
# Parameters shown in Table 1
Plot.dcl.par(my.bdcl.par,type.inflat='BDCL')
# BDCL Predictions by diagonals (future calendar years)
preds.bdcl.diag<-dcl.predict(my.bdcl.par,NtriangleBDCL,num.dec=0)

DCL documentation built on May 5, 2022, 5:06 p.m.