R for Non‑Life Insurance Mathematics and Statistics

Why R Matters in Non‑Life Insurance

Actuaries in property and casualty sectors face large data sets, complex loss models, and regulatory reporting. R offers a free, open‑source platform that integrates data manipulation, statistical modeling, and visualization, making it ideal for pricing, reserving, and capital adequacy tasks.

Core Packages for Actuarial Work

The following libraries form the backbone of most R‑based actuarial workflows:

• actuar – survival analysis, loss triangles, and stochastic reserving.
• actuarial – actuarial functions, mortality tables, and premium calculations.
• survival – time‑to‑event models for claim frequencies.
• ggplot2 – advanced visualizations for loss distributions.
• data.table – fast, memory‑efficient data handling.

Loss Triangle Construction and Stochastic Reserving

Constructing a loss triangle is the first step in many reserving models. Using data.table, an analyst can pivot raw claim data into a three‑dimensional array:

library(data.table) claims_dt <- fread("claims.csv") triangle <- dcast(claims_dt, Origin ~ Development, value.var = "Paid", fun.aggregate = sum)

With the triangle ready, the actuar package provides the chainladder function to apply stochastic chain‑ladder methods, yielding confidence intervals for reserves.

Example: Chain‑Ladder with Confidence Bands

library(actuar) reserves <- chainladder(triangle, method = "stochastic") print(reserves$chains)

Pricing Models: Frequency and Severity

Non‑life pricing often separates claim frequency (how often claims occur) from severity (the size of each claim). R handles both with generalized linear models (GLMs):

library(glmnet)

Frequency model

freq_fit <- glm(Claims ~ Age + Gender + PolicyType, family = poisson(link = "log"), data = training)

Severity model

sev_fit <- glm(SumPaid ~ Age + Gender + PolicyType, family = Gamma(link = "inverse"), data = training)

Predictive premium is the product of expected frequency and severity, adjusted by a load factor for expenses and profit.

Risk Modeling with Copulas and Simulation

Capturing dependence between claim types (e.g., auto and home) is critical. The copula package facilitates multivariate modeling:

library(copula) cop <- normalCopula(param = 0.6, dim = 2) samples <- rCopula(1000, cop)

Transform to marginal distributions

freq_samples <- qpois(samples[,1], lambda = 0.05) sev_samples <- qgamma(samples[,2], shape = 2, scale = 5000)

Monte Carlo simulation of aggregated loss yields tail‑risk metrics such as Value‑at‑Risk (VaR) and Tail Value‑at‑Risk (TVaR).

Regulatory Reporting and Automation

R can generate XML or JSON reports that conform to Solvency II or IFRS 17 formats. The jsonlite and XML packages help serialize actuarial outputs into the required schemas, enabling automated submission pipelines.

Performance Tips for Large Data Sets

• Use data.table over data.frame for speed.
• Parallelize GLM fitting with parallel or furrr.
• Store intermediate results in fst files to reduce memory churn.

Learning Path for Actuaries

1. Master R basics and data manipulation.

2. Study the actuar and actuarial packages through hands‑on exercises.

3. Build end‑to‑end projects: loss triangle → stochastic reserves → pricing → risk simulation.

4. Contribute to open‑source actuarial R packages to stay current with industry best practices.