extract.prior {DCL}

Extracting information about zero-claims and severity inflation

Description

A way of extracting information about zero-claims and severity development inflation through the DCL method applied to two counts triangles: number of payments and number of reported claims.

Usage

extract.prior(Xtriangle, Npaid, Ntriangle, Plots = TRUE , n.cal = NA ,
  Fj.X = NA , Fj.N = NA , Fj.Npaid = 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.

Npaid

A run-off (incremental) triangle with the number of payments. 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.))

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.))

Plots

Logical. If TRUE (default) it is showed a two by one plot showing the extracted severity inflation in the development direction and the probability of zero-claims for each underwriting period.

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.Npaid

Optional vector with lentgth m-1 with the development factors to calculate the chain ladder estimates from Npaid.

Fj.N

Optional vector with lentgth m-1 with the development factors to calculate the chain ladder estimates from Ntriangle.

Details

The function implements the strategy proposed in the paper by Martinez-Miranda, Nielsen, Verrall and Wuthrich (2013) to extract information for additional triangles (see "Section 5: An example showing how other data can be used to provide prior information in practice"). The derived severity inflation inflat.j does not extend to the tail. If you want provide the tail, by using dcl.predict.prior, the vector should be extended to have dimension 2m-1, otherwise the tail will be not provided (as was done in the cited paper).

Value

inflat.j

A vector with dimension m with the extracted severity inflation in the development direction.

Qi

A vector with dimension m with the extracted probability of zero-claims for undewriting period.

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

dcl.predict.prior, dcl.estimation

Examples

## Data application in Martinez-Miranda, Nielsen, Verrall and Wuthrich (2013)
data(NtrianglePrior)
data(NpaidPrior)
data(XtrianglePrior)

extract.prior(XtrianglePrior,NpaidPrior,NtrianglePrior)