Summarise redistributed large-loss experience

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.

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.

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.

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.

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.

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.

See also

redistribute_excess_loss()

Author

Martin Haringa