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Decompose claim amounts into capped and excess parts

Source: R/excess_loss.R
calculate_excess_loss.Rd

Large claims can distort risk-factor relativities and make pricing models unstable. calculate_excess_loss() separates each row in a portfolio into a capped claim amount and an excess part above a selected threshold.

Usage

calculate_excess_loss(data, claim_amount, threshold)

Arguments

data

A data.frame with portfolio-level or claim-level observations. Portfolio-level data can include policies without claims, for example rows where n_claims = 0 and the claim amount is zero.

claim_amount

Character string. Claim amount column.

threshold

Positive numeric scalar. Claims above this value contribute to the excess component. Claims below the threshold remain fully included in the capped claim amount.

Value

A data.frame with the original data and three added columns. The names are derived from claim_amount: <claim_amount>_capped, <claim_amount>_excess and <claim_amount>_is_excess.

Details

The capped claim amount can be used to model the base premium, while the excess component can be analysed, pooled or allocated separately. This allows the impact of large individual claims to be controlled without ignoring the associated cost.

The function is deliberately deterministic. It does not perform smoothing, credibility weighting, allocation or simulation. It simply decomposes each observed claim into:

$$ claim\_amount = claim\_amount\_capped + claim\_amount\_excess $$

where:

$$ claim\_amount\_excess = max(claim\_amount - threshold, 0) $$

and:

$$ claim\_amount\_capped = min(claim\_amount, threshold) $$

The output column names are derived from the column supplied through claim_amount. For example, if claim_amount = "incurred_loss", the added columns are incurred_loss_capped, incurred_loss_excess and incurred_loss_is_excess.

The resulting excess component can subsequently be allocated using allocate_excess_loss() and added back to the technical premium using apply_excess_loading().

Typical pricing workflow

A common workflow is:

  1. Select an excess threshold.

  2. Split claims into capped and excess components.

  3. Model frequency and severity using capped claim amounts.

  4. Allocate the excess-loss burden separately.

  5. Add the resulting excess loading back to the technical premium.

This approach reduces the influence of a small number of large claims on risk-factor relativities while ensuring that the total cost of excess losses remains reflected in the final premium.

Author

Martin Haringa

Examples

portfolio <- data.frame(
  policy_id = 1:4,
  n_claims = c(0, 1, 1, 0),
  claim_amount = c(0, 120000, 30000, 0)
)

calculate_excess_loss(
  portfolio,
  claim_amount = "claim_amount",
  threshold = 100000
)
#>   policy_id n_claims claim_amount claim_amount_capped claim_amount_excess
#> 1         1        0            0               0e+00                   0
#> 2         2        1       120000               1e+05               20000
#> 3         3        1        30000               3e+04                   0
#> 4         4        0            0               0e+00                   0
#>   claim_amount_is_excess
#> 1                  FALSE
#> 2                   TRUE
#> 3                  FALSE
#> 4                  FALSE