\documentclass[a4paper,11pt]{article}
%\VignetteIndexEntry{Claim-level reserving and back-testing: a short tour}
%\VignetteEngine{knitr::knitr}
%\VignetteEncoding{UTF-8}
\usepackage[margin=2.5cm]{geometry}
\usepackage{amsmath}
\usepackage{hyperref}
\title{\texttt{baggingReserve}: a short tour}
\author{Jan Janou\v{s}ek and Michal Pe\v{s}ta}
\begin{document}
\maketitle

<<setup, include=FALSE>>=
knitr::opts_chunk$set(comment = "#>", collapse = TRUE, fig.align = "center", fig.width = 6, fig.height = 4)
old_options <- options(width = 80, digits = 4, scipen = 8)
@

This vignette walks through the workflow of the package: a data contract that turns claims and
payment transactions into a claim-by-development-year panel, a recursion engine that completes
the payment history of every reported claim, by default with the regression trees and bagging of
Janou\v{s}ek and Pe\v{s}ta (2025), \emph{Bagging and regression trees in individual claims
reserving}, Statistical Papers 66(4), and a back-test against the payments that followed. It
uses the claims of types 2 and 3 of the shipped synthetic portfolio (generated with the article's
simulator under another seed; not the article's data) and few bootstrap replicates, so that it
builds quickly. The accompanying Journal of Statistical Software manuscript, shipped as the
vignette \texttt{baggingReserve-jss}, describes the method and the design in full and back-tests
the method on the whole portfolio, on an illustrative motor third-party liability dataset (a subset of an insurer's data, drawn in an undocumented way and published in a public code repository) and on
further synthetic portfolios.

\section*{From claims and payments to a panel}

Two tables enter: one row per claim reported by the valuation date and one row per payment
transaction. The constructor enforces the valuation date on both, sums payments per claim and
development year, keeps recoveries, marks the cells after the valuation date as \texttt{NA} and
refuses input it cannot interpret.
<<panel>>=
library("baggingReserve")
data("synthetic_claims", "synthetic_payments", package = "baggingReserve")
cl <- synthetic_claims[synthetic_claims$Type %in% c("2", "3"), ]
pay <- synthetic_payments[synthetic_payments$Id %in% cl$Id, ]
panel <- claims_panel(cl, pay, t = 12, L = 11, features = c("Type", "Age", "AccWeekday"))
panel
round(as_triangle(panel) / 1e6, 1)
@

\section*{One pruned tree per development year}

The tree for development year $l$ (the package calls this index its \texttt{period}) predicts
the payment of the next development year, $X_{l+1}$, of a reported claim from its features, its
reporting delay and $X_0, \dots, X_l$; the trees are applied recursively to complete every
reported claim's history.
<<tree>>=
tree <- reserve_tree(panel, seed = 1)
tree
pred_tree <- predict(tree)
pred_tree
@

By default each predicted mean is plugged into the history used by the next tree, as in the
source article. Where the occurrence of a payment depends on the payment history, this biases
the payments after next year; simulating the payments instead (\texttt{completion = "draw"})
removes that mechanism, and it is the recommended completion for totals beyond next year. The
next year's payments are the same in expectation under both.
<<tree-draw>>=
pred_draw <- predict(tree, completion = "draw", R = 50, seed = 1)
cbind(plug_in = calendar_year_payments(pred_tree)[, 1],
      simulated = rowMeans(calendar_year_payments(pred_draw)))[c(1, 11, 12), ]
@

\section*{Bagging, out-of-bag scores, IBNR}

\texttt{bag\_reserve()} grows a bootstrap tree per development year and replicate, completes
the panel once per replicate, and records the out-of-bag predictions (``votes''). The $B = 20$
replicates used here demonstrate the interface; they are far too few for stable tail quantiles.
The manuscript uses 1000 for its live run and 10,000 for the deposited full run.
<<bagging>>=
bag <- bag_reserve(panel, B = 20, seed = 2026)
oob_score(bag)[, c("period", "n_train", "coverage", "oob_score")]
res <- ibnr_reserve(predict(bag), claim_counts(panel))
res
summary(res, probs = c(0.025, 0.5, 0.975))$tables$total
@

The quantiles are empirical quantiles, over the replicates, of the reserve predicted by one set
of unpruned bootstrap trees (one per development year); they describe this resampling variation
and are neither prediction intervals for the future payments nor confidence intervals for the
bagged mean. For a bagged fit the completion is chosen when fitting:
<<bagging-draw>>=
bag_draw <- bag_reserve(panel, B = 20, seed = 2026, completion = "draw")
res_draw <- ibnr_reserve(predict(bag_draw), claim_counts(panel))
@

\section*{Comparators and back-test}

The shipped truth allows a back-test against the payments that actually followed. The truth
tables must describe the same portfolio as the prediction, including the claims reported after
the valuation date: a subset is selected by the same criterion as the panel (here the claim
type), never by the identifiers of the reported claims. The chain ladder on the panel's paid
triangle is scored against the same truth.
<<backtest>>=
data("synthetic_claims_full", "synthetic_payments_full", package = "baggingReserve")
cl_full <- synthetic_claims_full[synthetic_claims_full$Type %in% c("2", "3"), ]
pay_full <- synthetic_payments_full[synthetic_payments_full$Id %in% cl_full$Id, ]
cl_ref <- chain_ladder(as_triangle(panel))
bt <- backtest(res, cl_full, pay_full, reference = cl_ref)
bt$tables$total[, c("calendar", "truth", "predicted", "rel_error", "reference_rel_error")]
bt_draw <- backtest(res_draw, cl_full, pay_full)
bt_draw$tables$total[c(1, 12), c("calendar", "truth", "predicted", "rel_error")]
@

<<plot, fig.cap="Predicted payments by calendar year with the realised payments.">>=
plot(res, "calendar", truth = setNames(bt$tables$total$truth, bt$tables$total$calendar))
@

A back-test at one valuation date is one draw of the error. Valuing the data at several earlier
dates (\texttt{claims\_panel(..., future\_payments = "drop")}, see the manuscript) gives an
empirical distribution of the errors of the claim-level method and of the chain ladder on one's
own data. These errors are a descriptive diagnostic, not independent validation samples: the
valuation dates share claims and payments, and the horizon usually changes with the date, so they
are dependent and do not give a calibrated predictive distribution.

<<restore-options, include=FALSE>>=
options(old_options)
@

\end{document}