dcl.boot {DCL}

Bootstrap distribution: the full cashflow

Description

Provide the distribution of the IBNR, RBNS and total (RBNS+IBRN) reserves by calendar years and rows using bootstrapping.

Usage

dcl.boot( dcl.par , sigma2 , Ntriangle , boot.type = 2 , B = 999 , 
  Tail = TRUE , summ.by = "diag" , Tables = TRUE , num.dec = 2 , n.cal = NA)

Arguments

dcl.par

A list object with the estimated parameters: the value returned by the functions dcl.estimation, bdcl.estimation or idcl.estimation.

sigma2

Optional. The variance of the individual payments in the first underwriting period.

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 be the same triangle used to get the value passed by the argument dcl.par.

boot.type

Choose between values 1, to provide only the variance process, or 2 (default), to take into account the uncertainty of the parameters.

B

The number of simulations in the bootstrap algorithm. The defaul value is 999.

Tail

Logical. If TRUE (default) the tail is provided.

summ.by

A character value such as "diag", "row" or "cell".

Tables

Logical. If TRUE (default) it is showed a table with the summary (mean, standard deviation, 1%, 5%, 50%, 95%, 99%) of the distribution of the outstanding liabilities in the future calendar periods (if summ.by="diag") or by underwriting period (if summ.by="row").

num.dec

Number of decimal places used to report numbers in the tables. Used only 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).

Details

If the calculated severity variance using the function dcl.estimation is not a valid estimate then it is recommended to provide directly this value through the argument sigma2. It can be calculated using the function var applied to a pilot sample of individual payments observed in the first underwriting period.

Value

array.rbns.boot

An array with dimensions (m,2m-1,B) (m being the dimension of the input triangles in DCL). Each array.rbns.boot[,,b] is a matrix, with m rows and 2m-1 columns, having the bootstrapped outstanding RBNS numbers as the entries (for b=1,...,B).

Mat.rbns

A matrix with B rows and 2m columns. Each Mat.rbns[b,] is a vector with elements being the outstanding liabilities for RBNS claims in the future calendar periods (sums by diagonals), and last value is the RBNS reserve (overall sum).

array.ibnr.boot

An array with dimensions (m,2m-1,B) (m being the dimension of the input triangles in DCL). Each array.ibnr.boot[,,b] is a matrix, with m rows and 2m-1 columns, having the bootstrapped outstanding IBNR numbers as the entries (for b=1,...,B).

Mat.ibnr

A matrix with B rows and 2m columns. Each Mat.ibnr[b,] is a vector with elements being the outstanding liabilities for IBNR claims in the future calendar periods (sums by diagonals), and last value is the RBNS reserve (overall sum).

Mat.total

A matrix with B rows and 2m columns. Each Mat.total[b,] is a vector with elements being the outstanding liabilities for total(=RBNS+IBNR) claims in the future calendar periods (sums by diagonals), and last value is the RBNS reserve (overall sum).

summ.rbns

A dataframe with the summary of the RBNS distribution. Only if Tables=TRUE.

summ.ibnr

A dataframe with the summary of the IBNR distribution. Only if Tables=TRUE.

summ.total

A dataframe with the summary of the total(=RBNS+IBNR) distribution. Only if Tables=TRUE.

Note

If boot.type=2 the function will take some time to perform the calculations. It increases with the dimension of the triangles and the specified number of simulations B.

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.

See Also

Plot.cashflow, dcl.boot.prior

Examples

# Results described in the data application by Martinez-Miranda, Nielsen and Verrall (2012)
data(NtriangleDCL)
data(XtriangleDCL)

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

# Full cashflow considering the tail (only the variance process)
# Below only B=200 simulations to be faster in the example
boot1<-dcl.boot(dcl.par=est,Ntriangle=NtriangleDCL,boot.type=1,B=200)
Plot.cashflow(boot1)

# Full cashflow with tail and taking into account the parameters uncertainty
# and B=999 simulations. Do not run it unless you can wait about one minute
# boot2<-dcl.boot(dcl.par=est,Ntriangle=NtriangleDCL,boot.type=2)
# Plot.cashflow(boot2)