dcl.boot.prior {DCL} | R Documentation |
Bootstrap distribution (the full cashflow) adding prior knowledge
Description
Provide the distribution of the IBNR, RBNS and total (RBNS+IBRN) reserves by calendar years and rows using bootstrapping.
Usage
dcl.boot.prior( Xtriangle , Ntriangle , sigma2 , mu , inflat.i , inflat.j , Qi ,
Model = 2 , adj = 1 , boot.type = 2, B = 999 ,
Tail = TRUE , summ.by = "diag", Tables = TRUE, num.dec = 2 , n.cal = NA ,
Fj.X = NA , Fj.N = 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 |
sigma2 |
Optional. The variance of the individual payments in the first underwriting period. |
mu |
Optional. The mean of the individual payments in the first underwriting period. |
inflat.i |
Optional. A vector with dimension m (the dimension of the input triangles) specifying the severity inflation in the underwriting direction. |
inflat.j |
Optional. A vector with dimension m specifying the severity inflation in the development direction. If not specified it will be assumed to be 1 and then the severity mean not depending on the development period. |
Qi |
Optional. A vector with dimension m specifying the probability of zero-claims for each underwriting period. If not specified then it will be assumed no zero-payments. |
Model |
Possible values are 0, 1 or 2 (default). See |
adj |
Method to adjust the estimated delay parameters for the distributional model. It should be 1 (default value) or 2. See |
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 |
summ.by |
A character value such as |
Tables |
Logical. If |
num.dec |
Number of decimal places used to report numbers in the tables. Used only if |
n.cal |
Integer specifying the number of most recent calendars which will be used to calculate the development factors. By default |
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 |
Fj.N |
Optional vector with lentgth m-1 with the development factors to calculate the chain ladder estimates from |
Details
If proper values are provided for the arguments sigma2
, mu
, inflat.i
, inflat.j
and Qi
then, they will be considered fixed as prior knowledge. Otherwise, if not specified, inflat.j
will be assumed to be a vector of ones, Qi
a vector of zeros, and the rest will be estimated using dcl.estimation
.
Value
array.rbns.boot |
An array with dimensions (m,2m-1,B) (m being the dimension of the input triangles in DCL). Each |
Mat.rbns |
A matrix with B rows and 2m columns. Each |
array.ibnr.boot |
An array with dimensions (m,2m-1,B) (m being the dimension of the input triangles in DCL). Each |
Mat.ibnr |
A matrix with B rows and 2m columns. Each |
Mat.total |
A matrix with B rows and 2m columns. Each |
summ.rbns |
A dataframe with the summary of the RBNS distribution. Only if |
summ.ibnr |
A dataframe with the summary of the IBNR distribution. Only if |
summ.total |
A dataframe with the summary of the total(=RBNS+IBNR) distribution. Only if |
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., Verrall, R. and Wuthrich, M.V. (2013) Double Chain Ladder, Claims Development Inflation and Zero Claims. Scandinavian Actuarial Journal. In press.
See Also
Examples
## Data application by in Martinez-Miranda, Nielsen, Verrall and Wuthrich (2013)
data(NtrianglePrior)
data(NpaidPrior)
data(XtrianglePrior)
## Extract information about zero-claims and severity dev. inflation
my.priors<-extract.prior(XtrianglePrior,NpaidPrior,NtrianglePrior,Plots=FALSE)
my.inflat.j<-my.priors$inflat.j
my.Qi<-my.priors$Qi
## Bootstrap cashflow incorporating prior knowledge about
## severity inflation and zero claims
# Only variance process
# Below only B=200 simulations for a fast example
dist.priorC.I<-dcl.boot.prior(NtrianglePrior,XtrianglePrior,
inflat.j=my.inflat.j,Qi=my.Qi,adj=2,Tail=FALSE,boot.type=1,B=200)
Plot.cashflow(dist.priorC.I)
## Try to compare with DCL with no prior knowledge:
# Only variance process
# dist.dcl.I<-dcl.boot.prior(NtrianglePrior,XtrianglePrior,adj=2,
# Tail=FALSE,boot.type=1)
# Plot.cashflow(dist.dcl.I)