ItriangleBDCL | R Documentation |
Real motor data from a major insurer. It is a yearly run-off (incremental) triangle consisting of the incurred data during 19 years. These data were used in the empirical illustration provided by Martinez-Miranda, Nielsen and Verrall (2013).
data(ItriangleBDCL)
Matrix with dimension 19 by 19: 19 undewriting years and 19 development years.
Martinez-Miranda, M.D., Nielsen, J.P. and Verrall, R. (2013) Double Chain Ladder and Bornhuetter-Fergusson. North American Actuarial Journal, 17(2), 101-113.
data(ItriangleBDCL) data(XtriangleBDCL) m<-nrow(XtriangleBDCL) clm.I<-clm(ItriangleBDCL) alpha.I<-clm.I$alpha # The total paid for each accident year in the past Ri.X<-rowSums(XtriangleBDCL,na.rm=TRUE) # Incurred outstanding numbers Ri.CL.incurred<-alpha.I-Ri.X Total.CL.incurred<- sum(Ri.CL.incurred,na.rm=TRUE) ## Compare with CL on paid data clm.X<-clm(XtriangleBDCL) Xhat<-as.matrix(clm.X$triangle.hat) Ri.CL.paid<-rowSums(Xhat)-rowSums(XtriangleBDCL,na.rm=TRUE) Total.CL.paid<- sum(Ri.CL.paid,na.rm=TRUE) # the predictions by rows data.frame(underw.year=c(1:m,"Total"),CLM.paid=c(Ri.CL.paid,Total.CL.paid), CLM.incurred=round(c(Ri.CL.incurred,Total.CL.incurred),4)) # now the predictions by diagonals inflat.factor<-Ri.CL.incurred/Ri.CL.paid inflat.factor[Ri.CL.paid==0]<-1 # the lower triangle from incurred chain ladder is defined as: Ihat<-Xhat for (i in 1:m) Ihat[i,]<-Xhat[i,]*inflat.factor[i] # now the sums by diagonals Diag.CL.paid<-sapply(split(Xhat, row(Xhat)+col(Xhat)), sum, na.rm=TRUE) Dclm.paid<-c(Diag.CL.paid[-(1:m)]) Total.CL.paid<- sum(Dclm.paid,na.rm=TRUE) Dclm.paid<-c(Dclm.paid,Total.CL.paid) Diag.CL.inc<-sapply(split(Ihat, row(Ihat)+col(Ihat)), sum, na.rm=TRUE) Dclm.inc<-c(Diag.CL.inc[-(1:m)]) Total.CL.inc<- sum(Dclm.inc,na.rm=TRUE) Dclm.inc<-c(Dclm.inc,Total.CL.inc) # A table with the chain ladder predictions (paid and incurred data) data.frame(Future.years=c(1:(m-1),'Tot.'), clm.paid=round(Dclm.paid),clm.incurred=round(Dclm.inc))
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