Derive insurance tariff segments — derive_tariff

Derives data-driven tariff segments for a continuous risk factor from a fitted "riskfactor_gam" object produced by risk_factor_gam(). The segments help translate a smooth GAM response pattern into practical categorical rating factors for a GLM tariff.

Usage

derive_tariff_segments(
  object,
  complexity = 0,
  max_iterations = 10000,
  population_size = 200,
  seed = 1,
  alpha = NULL,
  niterations = NULL,
  ntrees = NULL
)

Arguments

object: An object of class "riskfactor_gam", produced by risk_factor_gam(). Objects with the old "fitgam" class are still supported for backward compatibility.
complexity: Numeric. Controls the complexity penalty used when deriving segments. Higher values generally yield fewer tariff segments. Default = 0.
max_iterations: Integer. Maximum number of search iterations used by the underlying grouping algorithm. Default = 10000.
population_size: Integer. Number of candidate trees used by the underlying grouping algorithm. Default = 200.
seed: Integer, seed for the random number generator (for reproducibility).
alpha: Deprecated. Use complexity instead.
niterations: Deprecated. Use max_iterations instead.
ntrees: Deprecated. Use population_size instead.

Value

A list of class "tariff_segments" with components:

gam_prediction: Data frame with the fitted GAM curve.
risk_factor: Name of the continuous risk factor.
model_type: Model type: "frequency", "severity", or "pure_premium".
classification_data: Data frame used to derive the segments.
risk_factor_values: Observed risk factor values in portfolio row order.
segment_boundaries: Numeric vector with segment boundaries.
assigned_segments: Factor with the tariff segment assigned to each observed risk factor value.

For backward compatibility, the old components prediction, x, model, data, x_obs, splits, class_boundaries, assigned_groups, and tariff_classes are also returned.

Details

Evolutionary trees (via evtree::evtree()) are used as a technique to bin the fitted GAM object into candidate tariff segments. This method is based on the work by Henckaerts et al. (2018). See Grubinger et al. (2014) for details on the parameters controlling the evtree fit.

References

Antonio, K. and Valdez, E. A. (2012). Statistical concepts of a priori and a posteriori risk classification in insurance. Advances in Statistical Analysis, 96(2), 187–224. doi:10.1007/s10182-011-0152-7

Grubinger, T., Zeileis, A., and Pfeiffer, K.-P. (2014). evtree: Evolutionary learning of globally optimal classification and regression trees in R. Journal of Statistical Software, 61(1), 1–29. doi:10.18637/jss.v061.i01

Henckaerts, R., Antonio, K., Clijsters, M., & Verbelen, R. (2018). A data driven binning strategy for the construction of insurance tariff classes. Scandinavian Actuarial Journal, 2018(8), 681–705. doi:10.1080/03461238.2018.1429300

Wood, S.N. (2011). Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. JRSS B, 73(1), 3–36. doi:10.1111/j.1467-9868.2010.00749.x

Author

Martin Haringa

Examples

if (FALSE) { # \dontrun{
library(dplyr)

# Recommended new usage (SE)
age_segments <- risk_factor_gam(MTPL,
                                risk_factor = "age_policyholder",
                                claim_count = "nclaims",
                                exposure = "exposure") |>
  derive_tariff_segments()

MTPL |>
  add_tariff_segments(age_segments, name = "age_policyholder_segment")
} # }