Actuarial Tools for Insurance Pricing Models • insurancerating

insurancerating provides actuarial tools and building blocks for analysing, modelling, refining, and validating insurance rating models in R.

The package is designed around common GLM-based pricing tasks and focuses on the translation of statistical model output into interpretable and controllable tariff structures.

Scope

The package supports common tasks that often occur in actuarial pricing work:

exploratory analysis of risk factors
estimation of GLM-based pricing models
controlled refinement of model coefficients
construction and interpretation of tariff structures
evaluation of model performance and stability

The focus is on reproducibility, interpretability, and consistency across models.

Installation

Install the CRAN version:

install.packages("insurancerating")

Or development version:

# install.packages("remotes")
remotes::install_github("MHaringa/insurancerating")

Quick example

library(insurancerating)

# Factor analysis
fa <- factor_analysis(
  MTPL,
  risk_factors = "zip",
  claim_count = "nclaims",
  exposure = "exposure",
  claim_amount = "amount"
)

autoplot(
  fa,
  metrics = c("frequency", "average_severity", "risk_premium")
)

Factor analysis plot showing frequency, average severity and risk premium by ZIP code.

# Fit model
mod <- glm(
  nclaims ~ zip,
  offset = log(exposure),
  family = poisson(),
  data = MTPL
)

rating_table(mod)

##   risk_factor       level   est_mod
## 1 (Intercept) (Intercept) 0.1402024
## 2         zip           0 1.0000000
## 3         zip           1 1.0254064
## 4         zip           2 0.9238016
## 5         zip           3 0.9757522

# Refine coefficients
zip_df <- data.frame(
  zip = c("0", "1", "2", "3"),
  zip_adj = c(0.90, 0.95, 1.00, 1.10)
)

mod_refined <- prepare_refinement(mod) |>
  add_restriction(zip_df) |>
  refit()

rating_table(mod_refined)

##   risk_factor       level est_mod_refined exposure
## 1 (Intercept) (Intercept)        0.136653       NA
## 2     zip_adj           0        0.900000      207
## 3     zip_adj           1        0.950000    11081
## 4     zip_adj           2        1.000000     7783
## 5     zip_adj           3        1.100000     7588

Combining Building Blocks

A possible sequence of steps is:

factor_analysis()      # analyse portfolio
glm()                  # estimate model
prepare_refinement()   # apply adjustments
rating_table()         # interpret coefficients

Core components

Factor analysis

factor_analysis() provides aggregated portfolio metrics such as:

frequency
average severity
risk premium
loss ratio

These are used to assess the behaviour and credibility of risk factors.

Rating models

Models are estimated using widely used GLM specifications:

Poisson for frequency
Gamma for severity
Gamma (log-link) for premium

rating_table() expresses model output in terms of original factor levels.

Model output can be adjusted using:

prepare_refinement(model) |>
  add_smoothing(...) |>
  add_restriction(...) |>
  add_relativities(...) |>
  refit()

This step is used to impose structure or incorporate expert judgement.

Model structure

extract_model_data(model)
rating_grid(model)

These functions expose the underlying model structure and allow aggregation at model-point level.

Validation

model_performance(model)
bootstrap_performance(model, data)

Used to assess predictive accuracy and stability.

Notes

This package is intended for general actuarial pricing work. It does not contain proprietary models, data, or business logic.

Learn more

Full documentation and examples are available in the articles:

insurancerating