Decompose claim amounts into capped and excess parts — calculate_excess

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

Usage

calculate_excess_loss(data, claim_amount, threshold)

Arguments

data: A data.frame with claim-level observations.
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 the columns claim_amount, capped_claim_amount, excess_claim_amount and is_excess_claim.

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:

$$ claim\_amount = capped\_claim\_amount + excess\_claim\_amount $$

where:

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

and:

$$ capped\_claim\_amount = min(claim\_amount, threshold) $$

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:

Select an excess threshold.
Split claims into capped and excess components.
Model frequency and severity using capped claim amounts.
Allocate the excess-loss burden separately.
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

claims <- data.frame(
  claim_amount = c(1000, 120000, 30000)
)

calculate_excess_loss(
  claims,
  claim_amount = "claim_amount",
  threshold = 100000
)
#>   claim_amount capped_claim_amount excess_claim_amount is_excess_claim
#> 1         1000               1e+03                   0           FALSE
#> 2       120000               1e+05               20000            TRUE
#> 3        30000               3e+04                   0           FALSE