Aggregate excess

The aggregate excess applies the attachment and limit to the total loss across all occurrences in a trial, not to individual occurrences. First sum, then apply the layer:

$$L_j^{\text{gross}} = \min\left(\max\left(\sum_{(t,e)} L_{j,t,e}^{\text{subject}} - A, 0\right), \ell\right)$$

The key difference from occurrence excess: occurrences accumulate against the attachment. Once the aggregate exceeds the attachment, the layer begins to pay. Once cumulative gross reaches the limit, coverage is exhausted.

Note the granularity change: occurrence excess preserves per-occurrence rows in its output, while aggregate excess collapses all occurrences within a trial into a single trial-level result. This resolution change matters when composing building blocks — downstream components receive trial-level data, not occurrence-level.

Applied to Trial 9’s subject in isolation at $100M xs $200M, the occurrences accumulate over the year. The cumulative subject loss crosses the $200M aggregate attachment in the autumn; the contract then pays the excess up to the $100M limit. Trial 9’s total subject is $272.1M, so the gross is $72.1M — the portion of the aggregate above the attachment:

Earthquake Hurricane Cumulative aggregate

Aggregate excess (100M xs 200M) on Trial 9's subject. The red line is the cumulative subject loss across the year; it crosses the $200M attachment and ends at $272.1M, so the contract pays $72.1M (the layer would cap at $300M = attachment + limit).

Trial 9	Value
Aggregate subject	$272.1M
Aggregate attachment	$200M
Gross (excess of attachment, capped at $100M)	$72.1M

helios_re/aggregate_excess.py Python

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Across all 20 trials, only the heaviest years pierce the $200M aggregate attachment, and the worst exhaust the $100M limit:

Aggregate excess EP curves: SunCoast subject vs 100M xs 200M on the trial aggregate. Fourteen of 20 trials exceed the $200M attachment; seven reach the $100M limit.

The aggregate excess is the whole of an AggXoL and the annual cap of a CatXoL (where the attachment is zero and the limit encodes the reinstatements).