dcl.predict {DCL}

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.

See Also

dcl.estimation, bdcl.estimation, idcl.estimation, dcl.predict.prior

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)