lossratio

Loss ratio analysis and projection for insurance experience data.

Overview

lossratio is a toolkit for long-term health insurance loss ratio analysis from long-format experience data — one row per (cohort × dev × demographic) cell with loss and risk premium columns. Multi-year health policies emit loss slowly: age-to-age factors are unstable in early development, exposure (≈ risk premium) is the most reliable anchor for projection, and structural shifts from product redesigns, underwriting changes, or regulatory reforms accumulate across cohorts. The package’s defaults — stage-adaptive projection, exposure-driven early development, cohort regime detection (regime: a homogeneous group of cohorts that share similar loss dynamics) — are tuned for this setting. The same tools apply to any cumulative loss / exposure framework (mortality, morbidity, general claims).

It provides:

• Three aggregation frameworks of the experience data: cohort × dev (Triangle), calendar period (Calendar), and portfolio total (Total)
• Age-to-age (ATA) and exposure-driven (ED) development modeling
• Chain ladder projection (fit_cl) and loss ratio projection (fit_lr) with three methods:
  • "sa" — stage-adaptive (default): exposure-driven before maturity, chain ladder after
  • "ed" — exposure-driven for all development periods
  • "cl" — classical chain ladder (Mack model)
• Cohort regime detection for structural breaks (detect_cohort_regime)
• Diagnostic and triangle visualisations

Expected input

A long-format data.frame / data.table with at minimum:

Column	Meaning	Example
cohort	Underwriting / accident period (any granularity)	uym, uy
dev	Development period since cohort start	elap_m, elap_y
loss	Incremental claim amount in the cell	numeric
rp	Incremental risk premium (expected loss) in the cell	numeric
group	Optional — coverage, product, age band, gender, etc.	character / factor

as_experience() validates the schema and coerces date columns; build_triangle() then aggregates to the canonical cohort × dev structure with cumulative columns and derived ratios.

Installation

# devtools
devtools::install_github("seokhoonj/lossratio")

# remotes
remotes::install_github("seokhoonj/lossratio")

The package depends on seokhoonj/instead and seokhoonj/ggshort (installed automatically via Remotes:).

Quick Start

library(lossratio)

# Built-in calibrated synthetic experience data
# (per-coverage dev curve calibrated to a real portfolio's broad shape;
# cell-level values and cohort patterns are randomly generated)
data(experience)
exp <- as_experience(experience)

# Build the canonical cohort × dev structure
tri <- build_triangle(exp, group_var = cv_nm)

plot(tri)              # cohort trajectories
plot_triangle(tri)     # cell heatmap

# Age-to-age and exposure-driven development
ata <- build_ata(tri, value_var = "closs"); fit_ata(ata)
ed  <- build_ed(tri);                       fit_ed(ed)

# Chain ladder fit
cl <- fit_cl(tri, value_var = "closs", method = "mack")
plot(cl, type = "projection")

# Loss ratio fit (stage-adaptive by default)
lr <- fit_lr(tri, method = "sa")
plot(lr, type = "clr")
summary(lr)

# Structural change across cohorts
detect_cohort_regime(tri[cv_nm == "SUR"], K = 12, method = "ecp")

Aggregation Frameworks

The same long-format experience data can be viewed three ways:

Builder	Output object	Dimension	Use case
build_triangle()	Triangle	cohort × dev (2D)	Chain ladder, ED, SA projection
build_calendar()	Calendar	calendar period (1D)	Calendar-year trend / diagonal effect
build_total()	Total	portfolio total (0D, per group)	High-level comparison across groups

After build_triangle, downstream columns are standardized to cohort and dev regardless of input granularity (uym / uyq / uy, etc.). Original column names and granularity are preserved as attributes (cohort_var, cohort_type, dev_var, dev_type).

Methods

Stage-Adaptive

fit_lr(method = "sa") (default). Hybrid of exposure-driven and chain ladder, switching at the maturity point per group:

• Before maturity: exposure-driven projection $\Delta C^L = g_k \cdot C^P_k$ — anchors the estimate to premium volume while age-to-age factors are volatile.
• After maturity: chain ladder projection $C^L_{k+1} = f_k \cdot C^L_k$ — preserves the cohort’s observed level once age-to-age factors stabilise.

Exposure-Driven

fit_lr(method = "ed"). All future loss increments use exposure (risk premium) as the denominator. Suitable when age-to-age factors are uninformative or unstable across the full development.

Chain Ladder

fit_lr(method = "cl") or fit_cl(). Classical Mack chain ladder with optional log-linear tail factor and analytic Mack standard errors.

Visualisation

Both S3 generics dispatch on object class:

plot(x)              # base plot generic — line / panel diagnostics
plot_triangle(x)     # lossratio generic — cell heatmap layout

plot() and plot_triangle() work uniformly across Triangle, Calendar, ATA, ATAFit, ED, EDFit, CLFit, LRFit, and CohortRegime objects.

Documentation

?build_triangle
?fit_lr
?detect_cohort_regime
vignette("regime-detection", package = "lossratio")

License

GPL (>= 2). See LICENSE.md.

Author

Seokhoon Joo (seokhoonj@gmail.com)