summary.excess_redistribution: Summarise redistributed large-loss experience

In insurancerating: Actuarial Tools for Insurance Pricing Models

Summarise redistributed large-loss experience

Description

Audit how much excess loss was contributed and received across portfolio segments after redistribute_excess_loss(). The summary shows whether a segment receives more large-loss cost than it contributes, or transfers part of its observed excess burden to other segments. The same audit is available for redistributed claims and separate excess loadings.

Usage

## S3 method for class 'excess_redistribution'
summary(object, by = NULL, ...)

Arguments

object	An object returned by redistribute_excess_loss().
by	Optional character string. Column used to group the audit. If NULL, use the original risk factor or return a portfolio-level summary.
...	Unused.

Details

redistributed_excess_contributed is the excess amount removed from selected large losses in a segment. redistributed_excess_received is the amount assigned back to claim-bearing rows in that segment. Their difference is:

net\_loss\_shift = received - contributed

A positive value means that the segment receives more redistributed loss than it contributed. A negative value means that it transfers loss to other segments. Across the full portfolio, net_loss_shift sums to zero, subject to numerical tolerance.

When by = NULL, the summary uses the risk_factor supplied to redistribute_excess_loss(). If no risk factor was supplied, one portfolio row is returned. Supply by to inspect a portfolio redistribution by another portfolio characteristic, for example summary(x, by = "sector").

The summary also exposes the loading calculation. For partial redistribution, ⁠<risk_factor>_excess_loading⁠ is blended with portfolio_excess_loading using ⁠<risk_factor>_credibility⁠. The resulting blended_excess_loading is multiplied by redistribution_scaling_factor to obtain final_redistribution_loading. Multiplying the final loading by the total receiving redistribution_weight gives redistributed_excess_received.

If by differs from the risk factor used in the redistribution, loading and credibility columns are receiving-weighted averages within each audit group. For separate-loading output, adjusted_loss is shown only as a reconciliation of retained plus allocated loss; it does not mean that the allocated amount was added to the row-level severity response.

Value

A data.frame with one row per audit group. The grouping column keeps its original name and type when by is used. The remaining columns are:

n_records

Number of portfolio records in the group.

claim_count

Number of claims in the group.

redistribution_weight

Total redistribution weight of rows that receive redistributed loss.

n_excess_records

Number of records with an observed amount above the threshold.

n_redistributed_excess_records

Number of records whose excess amount was actually contributed to the redistribution pool.

observed_loss

Observed claim cost before redistribution.

retained_loss

Claim cost retained at or below the threshold, including full claims excluded through redistribute_excess.

observed_excess_loss

Observed claim cost above the threshold, including excess from rows excluded through redistribute_excess.

redistributed_excess_contributed

Excess removed from selected large losses and contributed to the redistribution pool.

⁠<risk_factor>_excess_loading⁠

Excess loading estimated from the risk-factor-level experience, per unit of redistribution weight.

⁠<risk_factor>_credibility⁠

Weight assigned to the risk-factor loading. It is zero for portfolio redistribution, one for risk-factor redistribution and between zero and one for partial redistribution.

portfolio_excess_loading

Portfolio-wide excess loading per unit of redistribution weight.

blended_excess_loading

Risk-factor loading times credibility plus portfolio loading times one minus credibility.

redistribution_scaling_factor

Factor that preserves the total amount being redistributed after blending.

final_redistribution_loading

Blended loading multiplied by the redistribution scaling factor.

allocated_excess_loss

Absolute excess-loss amount allocated to the audit group.

average_excess_loading

Allocated excess loss per unit of total receiving redistribution weight.

redistributed_excess_received

Excess assigned to receiving claim-bearing rows.

net_loss_shift

Received minus contributed redistributed excess.

adjusted_loss

Claim cost after redistribution.

observed_average_claim

Observed loss divided by claim count.

adjusted_average_claim

Adjusted loss divided by claim count.

Author(s)

Martin Haringa

See Also

redistribute_excess_loss()

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