Bagging and Regression Trees for Individual Claims Reserving

Claim-level (individual) loss reserving in non-life insurance, and the means to check claim-level reserves against the payments that followed. A data contract turns a table of claims and a table of payment transactions into a claim-by-development-year panel at a valuation date; a recursion engine completes the payment history of every reported claim one development year ahead, with plugged-in means or simulated payments, for regression trees, their bootstrap aggregation (bagging) and user-supplied learners; payments for incurred-but-not-reported claims are added from chain-ladder claim counts and the average predicted payment per development year; and back-tests score a prediction and a reference method such as the chain ladder against realised payments by calendar year and component. The default estimator is the method of Janoušek and Pešta (2025) , one regression tree per development year with bagging for replicate predictions, whose spread describes the bootstrap resampling variation of the predictions of (by default unpruned) trees, and an out-of-bag diagnostic of the one-year regressions; for totals beyond next year simulated instead of plugged-in completion is recommended. Ships a reproducible synthetic individual-claims dataset generated with the individual claims simulator of Wang and Wüthrich, built on 'SynthETIC'.

baggingReserve

An R package for claim-level (individual) loss reserving and for checking claim-level reserves against the payments that followed. It has three parts:

• a data contract: claims_panel() turns a table of claims and a table of payment transactions, with your column names, into a claim-by-development-year panel at a valuation date; it enforces the valuation date on both tables, distinguishes observed zeros from future cells, keeps recoveries and claims without payments, and refuses input it cannot interpret;
• a recursion engine, shared by the single-tree fit (reserve_tree()), the bagged ensemble (bag_reserve()) and user-supplied learners (learner = , two_part_learner()), that completes the payment history of every reported claim one development year ahead, with plugged-in means (completion = "mean") or simulated payments (completion = "draw"); ibnr_reserve() adds the claims incurred but not reported (IBNR) from chain-ladder projections of the reporting counts;
• back-testing: backtest() scores a prediction, and a reference method such as the chain ladder, against realised payments by calendar year and separately for reported and IBNR claims.

The default estimator, a documented baseline that other learners can be measured against, is the method of Bagging and regression trees in individual claims reserving (J. Janoušek and M. Pešta, Statistical Papers 66(4), 2025, doi:10.1007/s00362-025-01715-9). A manuscript describing the package has been submitted to the Journal of Statistical Software; it ships as the vignette baggingReserve-jss. On the portfolios studied there, the standard chain ladder is more accurate than the default trees on most of them: the package is meant for finding out, with backtest(), whether claim-level information helps on your own data.

What the default method does

• Each reported claim carries static features (type, age of the insured, accident weekday, reporting delay d) and its yearly payment history X_0, …, X_l.
• For every development year l = 0, …, L−1 (called period in the package) one regression tree (rpart, pruned at the smallest cross-validated error) predicts X_{l+1} from the features and X_0, …, X_l, trained on the claims reported by development year l whose payment in year l+1 is already observed.
• The unobserved cells of every reported claim (closed claims included; status is not a predictor in the source article's specification) are filled recursively one development year ahead, earlier predictions feeding later features.
• Bagging replaces each tree by a bootstrap ensemble. A replicate takes one bootstrap tree from every development year and completes all histories; the point estimate is the bagged mean of the completed replicates, and the replicate quantiles describe the variation, under this resampling, of the reserve predicted by one set of unpruned bootstrap trees (they are neither prediction intervals nor confidence intervals for the bagged mean). The out-of-bag score per development year is a diagnostic of the one-year regressions.
• The IBNR component follows Theorem 1 of the source article: projected numbers of not-yet-reported claims (chain ladder on the reporting-count triangle) times the mean predicted payment per development year of the reported claims.

The default completion = "mean" plugs each predicted mean into the history used by the next tree, as the source article does. Where the occurrence of a payment depends on the payment history this biases the payments after next year, so for totals beyond next year use completion = "draw", which simulates the payments instead.

The per-claim reserves (claim_reserves()) add up to the aggregate, but they are not a reliable allocation between open and closed claims: the trees do not see the settlement status.

Data

The shipped data are synthetic and fully reproducible: the Wang & Wüthrich (2022) Individual Claims Simulator (GPL-3, built on SynthETIC) run on a yearly grid with seed 2026 — six claim types, twelve accident years, 62,904 closed + 8,213 RBNS = 71,117 reported claims and 2,588 IBNR claims at t = 12. This is a fresh portfolio from the same simulator family as the article's, not the article's data (which used another seed, ten accident years and valuation at t = 10); the manuscript's numbers are therefore not those of the article and are not meant to reproduce them.

synthetic_claims holds only what is observable at t = 12; the generated ultimate claim amount and payment count live in synthetic_claims_full alone. data-raw/make_synthetic_claims.R in the source repository regenerates the four .rda files from the vendored generator and records the call and versions in data-raw/GENERATION.txt.

Installation

# from CRAN (once released; version 0.1.1 is under review)
install.packages("baggingReserve")

# development version
# install.packages("remotes")
remotes::install_github("HeirOfIsildur/baggingReserve", build_vignettes = TRUE)

Interface

library("baggingReserve")
panel <- claims_panel(synthetic_claims, synthetic_payments, t = 12, L = 11,
                      features = c("Type", "Age", "AccWeekday"))
tree  <- reserve_tree(panel, seed = 1)                     # one pruned rpart per period l
bag   <- bag_reserve(panel, B = 100, seed = 2026, ncores = 4)
oob_score(bag)                                             # per-period OOB score, coverage, n
pred  <- predict(bag)                                      # future-cell payments, one column per replicate
res   <- ibnr_reserve(pred, claim_counts(panel))           # adds the IBNR component (Theorem 1)
summary(res)                                               # mean, sd, replicate quantiles per calendar year
calendar_year_payments(res)                                # next year ... development L, per replicate
plot(res, "next_year"); plot(res, "calendar")
cl    <- chain_ladder(as_triangle(panel))                  # aggregate baseline (standard chain ladder)
backtest(res, synthetic_claims_full, synthetic_payments_full, reference = cl)
# simulated completion, recommended for totals beyond next year
bag_draw <- bag_reserve(panel, B = 100, seed = 2026, ncores = 4, completion = "draw")

The article's variants are reachable by argument: ibnr_reserve(..., projection = "incremental_ratio", round = TRUE) and chain_ladder(..., projection = "incremental_ratio") use its incremental-ratio count projection and chain-ladder baseline; summary(..., type = 1) gives order-statistic quantiles.

Vignettes

• vignette("baggingReserve"): a short tour of the workflow on a part of the shipped portfolio.
• vignette("baggingReserve-jss"): the manuscript submitted to the Journal of Statistical Software (precompiled PDF).

Related repositories

• article-bagging-regression-trees — the Statistical Papers article (PDFs).
• master-thesis-bagging-regression-trees — the thesis the article grew from; its R script (rpart + ipred::bagging) is the ancestor of this package.

Citation

citation("baggingReserve")

Licence

GPL (≥ 3). The vendored generator in data-raw/IndividualClaimsSimulator/ of the source repository is GPL-3 by Melantha Wang and Mario V. Wüthrich and keeps its own licence file.