Actuarial Tools for Insurance Pricing Models • insurancerating

insurancerating provides functions for common actuarial pricing tasks in R, including portfolio analysis, GLM estimation, coefficient refinement and model diagnostics.

The package is organised around GLM-based pricing work and the translation of statistical model output into tariff structures that can be reviewed, documented and implemented. The functions can be used independently or combined into a workflow appropriate for the portfolio and pricing question.

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 appropriate combination of model choice, segmentation, refinement and validation depends on the product, data, portfolio composition and intended use of the tariff.

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 summaries describe observed portfolio experience. They help identify volume, heterogeneity and potentially unstable levels, but they do not adjust for correlations with other risk factors and are not fitted tariff relativities.

Rating models

Models are estimated using widely used GLM specifications:

Poisson for frequency
Gamma for severity
Gamma with a log link for severity or risk premium

rating_table() expresses fitted coefficients in terms of the original factor levels. When coefficients are exponentiated, they are shown as relativities.

Model output can be adjusted using:

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

Refinement records smoothing, restrictions, shrinkage, sublevel relativities and rebasing explicitly before the model is refitted. Shrinkage reduces differences between categorical relativities while preserving their selected weighted level. Rebasing changes which resulting tariff level equals 1 without changing the ratios between levels. These adjustments should be supported by the available experience, tariff interpretation or documented expert judgement.

Model structure

extract_model_data(model)
rating_grid(model)

These functions recover the data represented by a fitted model and construct observed model-point combinations. They are useful when predictions and tariff reviews must remain aligned with the estimation portfolio.

Validation

model_performance(model)
bootstrap_performance(model, data)

These functions compare response-scale error and information criteria and assess sensitivity under repeated sampling. They provide complementary diagnostics rather than an automatic model-selection rule.

Notes

The examples represent general actuarial pricing applications. Their modelling choices and thresholds are illustrative and should be assessed against the portfolio, data quality and governance requirements of the intended use.

Learn more

Full documentation and examples are available in the articles: