Apply an allocated excess-loss loading to a portfolio data set.
Usage
apply_excess_loading(
data,
allocation,
base_premium = "base_premium",
allocated_excess_loss = NULL,
allocated_loading = NULL,
weight = NULL,
output = c("premium", "rate")
)Arguments
- data
A data.frame containing the base premium or base rate.
- allocation
An object returned by
allocate_excess_loss().Character string. Column containing the base premium amount or base rate before the excess loading is added.
- allocated_excess_loss
Optional character string. Column in
allocation$datacontaining the allocated excess-loss amount in monetary terms. IfNULL,allocated_excess_lossis used.- allocated_loading
Optional character string. Column in
allocation$datacontaining the allocated excess loading per unit of allocation weight. IfNULL,allocated_loadingis used.- weight
Optional character string. Weight column used to convert between premium amounts and rates when
output = "rate".- output
Character string. Use
"premium"to return premium amounts or"rate"to return rates per unit of weight.
Value
A data.frame. With output = "premium", the result contains
base_premium, allocated_excess_loss, allocated_loading,
excess_loading and loaded_premium. With output = "rate", the result
contains base_rate, allocated_loading and loaded_rate.
Details
apply_excess_loading() is the final step in the excess-loss pricing workflow.
It does not cap claims, estimate excess losses or allocate the excess burden.
Instead, it takes the output of allocate_excess_loss() and adds the
allocated excess component back to the base premium or base rate.
The function is typically used after the base premium has been modelled on capped claim amounts. The excess loading then ensures that the cost of claims above the selected threshold is still reflected in the final technical premium.
Premium output
With output = "premium", the function adds the allocated excess loss in
monetary terms to the base premium:
$$ loaded\_premium = base\_premium + allocated\_excess\_loss $$
allocated_excess_loss is the row-level monetary amount of excess loss
allocated to each risk.
Rate output
With output = "rate", the function adds the allocated excess loading per
unit of weight to the base rate:
$$ loaded\_rate = base\_rate + allocated\_loading $$
Use this option when the base value represents a rate per exposure, premium unit, insured value or other allocation weight.
If the input column supplied through base_premium contains premium amounts
rather than rates, the function first converts the base premium to a rate:
$$ base\_rate = \frac{base\_premium}{weight} $$
Interpretation of allocation columns
allocated_excess_loss represents the monetary excess-loss burden allocated
to a row.
allocated_loading represents the excess loading per unit of allocation
weight.
In other words:
$$ allocated\_excess\_loss = allocated\_loading \cdot weight $$
This distinction is important when moving between premium amounts and rates.
Typical pricing workflow
A common workflow is:
Use
calculate_excess_loss()to separate capped and excess losses.Model the base premium using capped claim amounts.
Allocate the excess-loss burden using
allocate_excess_loss().Use
apply_excess_loading()to add the allocated excess component back to the base premium or base rate.
This produces a final technical premium that reflects both the modelled capped loss cost and the separately allocated excess-loss burden.
Examples
claims <- data.frame(
sector = rep(c("Industry", "Retail"), each = 4),
claim_amount = c(
1000, 120000, 30000, 8000,
2000, 150000, 40000, 6000
),
earned_exposure = rep(1, 8)
)
decomposed <- calculate_excess_loss(
claims,
claim_amount = "claim_amount",
threshold = 100000
)
decomposed$base_premium <- 500
allocation <- allocate_excess_loss(
decomposed,
excess_amount = "excess_claim_amount",
allocation_weight = "earned_exposure"
)
apply_excess_loading(
decomposed,
allocation,
base_premium = "base_premium"
)
#> sector claim_amount earned_exposure capped_claim_amount excess_claim_amount
#> 1 Industry 1000 1 1e+03 0
#> 2 Industry 120000 1 1e+05 20000
#> 3 Industry 30000 1 3e+04 0
#> 4 Industry 8000 1 8e+03 0
#> 5 Retail 2000 1 2e+03 0
#> 6 Retail 150000 1 1e+05 50000
#> 7 Retail 40000 1 4e+04 0
#> 8 Retail 6000 1 6e+03 0
#> is_excess_claim base_premium allocated_excess_loss allocated_loading
#> 1 FALSE 500 8750 8750
#> 2 TRUE 500 8750 8750
#> 3 FALSE 500 8750 8750
#> 4 FALSE 500 8750 8750
#> 5 FALSE 500 8750 8750
#> 6 TRUE 500 8750 8750
#> 7 FALSE 500 8750 8750
#> 8 FALSE 500 8750 8750
#> excess_loading loaded_premium
#> 1 8750 9250
#> 2 8750 9250
#> 3 8750 9250
#> 4 8750 9250
#> 5 8750 9250
#> 6 8750 9250
#> 7 8750 9250
#> 8 8750 9250
apply_excess_loading(
decomposed,
allocation,
base_premium = "base_premium",
weight = "earned_exposure",
output = "rate"
)
#> sector claim_amount earned_exposure capped_claim_amount excess_claim_amount
#> 1 Industry 1000 1 1e+03 0
#> 2 Industry 120000 1 1e+05 20000
#> 3 Industry 30000 1 3e+04 0
#> 4 Industry 8000 1 8e+03 0
#> 5 Retail 2000 1 2e+03 0
#> 6 Retail 150000 1 1e+05 50000
#> 7 Retail 40000 1 4e+04 0
#> 8 Retail 6000 1 6e+03 0
#> is_excess_claim base_premium base_rate allocated_loading loaded_rate
#> 1 FALSE 500 500 8750 9250
#> 2 TRUE 500 500 8750 9250
#> 3 FALSE 500 500 8750 9250
#> 4 FALSE 500 500 8750 9250
#> 5 FALSE 500 500 8750 9250
#> 6 TRUE 500 500 8750 9250
#> 7 FALSE 500 500 8750 9250
#> 8 FALSE 500 500 8750 9250