assess_excess_threshold: Assess possible excess-loss thresholds

In insurancerating: Actuarial Tools for Insurance Pricing Models

Assess possible excess-loss thresholds

Description

Compare candidate thresholds for capped severity and large-loss pricing work.

assess_excess_threshold() is a diagnostic helper. It does not choose a threshold automatically. It shows how many claims, how many records contain claim amounts above candidate thresholds, how much historical claim cost sits above those thresholds, and how much risk premium would remain after capping claims at each threshold.

The function is intended for portfolio-level data as well as claim-level data. Portfolio-level data can include policies without claims, for example rows where claim_count = 0 and the claim amount is zero. Use this before redistribute_excess_loss() to understand the effect of the threshold on the portfolio. The output is useful for tariff notes, pricing reviews and governance discussions around adjusted severity models.

Usage

assess_excess_threshold(
  data,
  claim_amount,
  thresholds,
  exposure = NULL,
  group = NULL,
  claim_count = NULL
)

Arguments

data	A data.frame with portfolio-level or claim-level observations. Portfolio-level data can include policies without claims.
claim_amount	Character string. Claim amount column.
thresholds	Numeric vector of candidate thresholds.
exposure	Optional character string. Exposure column. If supplied, risk premium before and after capping is calculated. The output column keeps this original name. If NULL, every record is counted as one exposure unit and the output contains an exposure column.
group	Optional character string. Grouping column used to assess thresholds by segment. The output column keeps this original name. If NULL, no grouping column is added.
claim_count	Optional character string. Claim-count column. If supplied, n_claims is calculated as the sum of this column. If NULL, records with claim_amount > 0 are counted as one claim and records with claim_amount == 0 as zero claims.

Details

The output can be used for two common follow-up analyses. First, aggregate the threshold assessment to portfolio level to calculate the average additional risk premium required to finance the excess layer. Second, after selecting a threshold, compare groups to see which parts of the portfolio benefit most from the excess protection.

Value

A data.frame with class "threshold_assessment" and columns:

group column

The original grouping column, such as sector, if group is supplied. This is the first column when grouping is used.

threshold

The excess threshold being assessed. Thresholds are shown in the same order as supplied in the thresholds argument.

exposure column

The original exposure column, such as policy_years, if exposure is supplied. If exposure = NULL, this column is named exposure and counts records.

n_claims

Total number of claims, calculated from claim_count or inferred from claim_amount > 0.

n_excess_records

Number of records with claim_amount > threshold. This counts records, not individual claims.

total_loss

Total claim amount before applying the threshold.

capped_loss

Total claim amount retained below or at the threshold.

excess_loss

Total claim amount above the threshold.

pure_premium_before

Risk premium before capping: total_loss / exposure.

pure_premium_after

Risk premium after capping: capped_loss / exposure.

premium_reduction

pure_premium_before - pure_premium_after, equivalent to excess_loss / exposure. This is positive when applying the threshold reduces the retained risk premium.

premium_reduction_ratio

premium_reduction / pure_premium_before. This is between 0 and 1 when pure_premium_before > 0; if pure_premium_before == 0, it is defined as 0.

Author(s)

Martin Haringa

Examples

portfolio <- data.frame(
  policy_id = 1:10,
  sector = rep(c("Industry", "Retail"), each = 5),
  claim_count = c(
    0, 1, 1, 1, 1,
    0, 1, 1, 1, 1
  ),
  claim_amount = c(
    0, 25000, 120000, 50000, 175000,
    0, 40000, 90000, 150000, 300000
  ),
  policy_years = rep(1, 10)
)

thresholds <- assess_excess_threshold(
  data = portfolio,
  claim_amount = "claim_amount",
  thresholds = c(25000, 50000, 100000, 150000),
  exposure = "policy_years",
  group = "sector",
  claim_count = "claim_count"
)

thresholds
if (requireNamespace("gt", quietly = TRUE)) {
  as_gt(thresholds)
}

# Calculate the average additional risk premium required to finance
# the excess portion of the claims.
thresholds |>
  dplyr::summarise(
    policy_years = sum(policy_years),
    excess_loss = sum(excess_loss),
    capped_loss = sum(capped_loss),
    extra_risk_premium = excess_loss / policy_years,
    risk_premium_increase = excess_loss / capped_loss,
    .by = "threshold"
  )

# After selecting a threshold, compare which groups benefit most
# from the excess protection.
selected_threshold <- thresholds |>
  dplyr::filter(threshold == 100000) |>
  dplyr::select(
    sector,
    threshold,
    policy_years,
    n_claims,
    n_excess_records,
    premium_reduction,
    premium_reduction_ratio
  ) |>
  dplyr::arrange(dplyr::desc(premium_reduction_ratio))

selected_threshold

# If claim_count is omitted, records with positive claim amounts are counted.
assess_excess_threshold(
  data = portfolio,
  claim_amount = "claim_amount",
  thresholds = 100000,
  exposure = "policy_years",
  group = "sector"
)

insurancerating documentation built on July 30, 2026, 5:09 p.m.