clmplus is an R package for implementing the age-period-cohort models for the claim development presented in the manuscript 'Replicating and extending chain-ladder via an age-period-cohort structure on the claim development in a run-off triangle' doi:10.1080/10920277.2025.2496725.
The models for the claim development available in the clmplus are based on the models for human mortality implemented in the StMoMo package. Users can either rely on our default models or set their own configuration for the claim development.
| Model | Lexis dimension | Claims reserving |
|---|---|---|
| a | age | development (chain-ladder model) |
| ac | age-cohort | development-accident |
| ap | age-period | development-calendar |
| apc | age-period-cohort | development-calendar-accident |
The developer version of clmplus can be installed from GitHub.
library(devtools)
devtools::install_github("gpitt71/clmplus")
The current version of clmplus can be installed from CRAN.
install.packages('clmplus')
In this brief example, we work with the sifa.mtpl data from the clmplus package. Further examples can be found in the package vignettes. The data set of cumulative claim payments is transformed into an AggregateDataPP object that pre-processes the data for claim development modelling.
library(clmplus)
data ("sifa.mtpl")
dataset = sifa.mtpl
datapp = AggregateDataPP(cumulative.payments.triangle = dataset, eta= 1/2)
Our models can be fit with the clmplus function.
a.model.fit=clmplus(datapp,
hazard.model = "a") # age-model replicates the chain ladder
ac.model.fit=clmplus(datapp,
hazard.model = "ac")
ap.model.fit=clmplus(datapp,
hazard.model = "ap")
apc.model.fit=clmplus(datapp,
hazard.model = "apc")
The plot function can be be used to explore the scaled deviance residuals of fitted models. Below, an example for the age-period-cohort (apc) model for the claim development.
plot(apc.model.fit)
Predictions are performed with the predict function.
a.model=predict(a.model.fit)
# clmplus reserve (age model)
sum(a.model$reserve)
#226875.5
ac.model=predict(ac.model.fit,
gk.fc.model = 'a',
gk.order = c(1,1,0))
# clmplus reserve (age-cohort model)
sum(ac.model$reserve)
#205305.7
ap.model= predict(ap.model.fit,
ckj.fc.model = 'a',
ckj.order = c(0,1,0))
# clmplus reserve (age-period model)
sum(ap.model$reserve)
#215602.8
apc.model= predict(apc.model.fit,
gk.fc.model = 'a',
ckj.fc.model = 'a',
gk.order = c(1,1,0),
ckj.order = c(0,1,0))
# clmplus reserve (age-period-cohort model)
sum(apc.model$reserve)
#213821.6
The fitted effect (and extrapolated) effects can be inspected with the plot function. We continue below the example with the apc model.
plot(apc.model)
APA Style
Pittarello, G., Hiabu, M., & Villegas, A. M. (2025). Replicating and Extending Chain-Ladder via an Age–Period–Cohort Structure on the Claim Development in a Run-Off Triangle. North American Actuarial Journal, 1-31.
BibTeX
@article{ ,
title={Replicating and Extending Chain-Ladder via an Age--Period--Cohort Structure on the Claim Development in a Run-Off Triangle},
author={Pittarello, Gabriele and Hiabu, Munir and Villegas, Andr{\'e}s M},
journal={North American Actuarial Journal},
pages={1--31},
year={2025},
publisher={Taylor \& Francis}
doi = {10.1080/10920277.2025.2496725},
}The most recent tutorials and replication files associated with the manuscript can be accessed via our project website.