dcl.predict: Pointwise predictions (RBNS/IBNR split)
In DCL: Claims Reserving under the Double Chain Ladder Model

dcl.predict

R Documentation

Pointwise predictions (RBNS/IBNR split)

Description

Pointwise predictions by calendar years and rows of the outstanding liabilities. The predictions are splitted between RBNS and IBNR claims.

Usage

dcl.predict( dcl.par , Ntriangle , Model = 2 , Tail = TRUE , 
  Tables = TRUE , summ.by="diag", num.dec = 2 )

Arguments

`dcl.par`	A list object with the estimated parameters: the value returned by the functions `dcl.estimation`, `bdcl.estimation` or `idcl.estimation`.
`Ntriangle`	Optional. 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 the `Xtriangle` (both in the same aggregation level (quarters, years,etc.)) used to derive `dcl.par`
`Model`	Possible values are 0, 1 or 2 (default). See more details below.
`Tail`	Logical. If `TRUE` (default) the tail is provided.
`Tables`	Logical. If `TRUE` (default) it is shown a table with the predicted outstanding liabilities in the future calendar periods (`summ.by="diag"`) or by underwriting period (`summ.by="row"`).
`summ.by`	A character value such as `"diag"`, `"row"` or `"cell"`.
`num.dec`	Number of decimal places used to report numbers in the tables. Used only if `Tables=TRUE`

Details

If Model=0 or Model=1 then the predictions are calculated using the DCL model parameters in assumptions M1-M3 (general delay parameters, see Martinez-Miranda, Nielsen and Verrall 2012). If Model=2 the adjusted delay probabilities (distributional model D1-D4) are considered. By choosing Model=0 the predictions are calculated ignoring the observed counts in Ntriangle (also if the Ntriangle is not specified). It should be specified to reproduce get the IBNR/RBNS split of classical paid chain ladder.

Choose summ.by="diag" to calculate the predicted outstanding liabilities in the future calendar periods (diagonal sums), summ.by="row" for sums by underwriting periods (row sums); or summ.by="cell" to get only the the individual cell predictions.

Value

`Xrbns`	A matrix with dimension m by 2m-1 (m being the dimension of the input triangles in DCL) having the outstanding RBNS numbers as the entries.
`Drbns`	A vector with dimension 2m-1 with elements being the outstanding liabilities for RBNS claims in the future calendar periods (sums by diagonals). The last value is the RBNS reserve (overall sum).
`Rrbns`	A vector with dimension m with elements being the outstanding liabilities for RBNS claims at each underwriting period (sums by rows). The last value is the RBNS reserve (overall sum).
`Xibnr`	A matrix with dimension m by 2m-1 (m being the dimension of the input triangles in DCL) having the outstanding IBNR numbers as the entries.
`Dibnr`	A vector with dimension 2m-1 with elements being the outstanding liabilities for IBNR claims in the future calendar periods (sums by diagonals). The last value is the IBNR reserve (overall sum).
`Ribnr`	A vector with dimension m with elements being the outstanding liabilities for IBNR claims at each underwriting period (sums by rows). The last value is the RBNS reserve (overall sum).
`Xtotal`	A matrix with dimension m by 2m-1 (m being the dimension of the input triangles in DCL) having the outstanding total (=RBNS+IBNR) numbers as the entries.
`Dtotal`	A vector with dimension 2m-1 with elements being the outstanding liabilities for all claims in the future calendar periods (sums by diagonals). The last value is the total (=RBNS+IBNR) reserve (overall sum).
`Rtotal`	A vector with dimension m with elements being the outstanding liabilities for all claims at each underwriting period (sums by rows). The last value is the total (=RBNS+IBNR) reserve (overall sum).

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., Verrall, R. and W|thrich, M.V. (2013) Double Chain Ladder, Claims Development Inflation and Zero Claims. Scandinavian Actuarial Journal.

Examples

## Data application by in Martinez-Miranda, Nielsen and Verrall (2012)

data(NtriangleDCL)
data(XtriangleDCL)

# Estimation of the DCL parameters described 
est<-dcl.estimation(XtriangleDCL,NtriangleDCL)

# with general delay parameters and ignoring Ntriangle to reproduce exactly chain ladder
pred1<-dcl.predict(dcl.par=est,Model=1,Tail=FALSE)

# with Modeled parameters (distributional Model) and ignoring Ntriangle
pred2<-dcl.predict(dcl.par=est,Model=2,Tail=FALSE)

# with Modeled parameters (distributional Model) using observed Ntriangle
pred3<-dcl.predict(dcl.par=est,Ntriangle=NtriangleDCL,Model=2,Tail=FALSE)

# providing the Tail, with Modeled parameters (distributional Model)
pred4<-dcl.predict(dcl.par=est,Ntriangle=NtriangleDCL,Model=2,Tail=TRUE)

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