Actuarial case explained
How is a catastrophe loss split between cedent and reinsurer?
Purpose
Decision informed
Choose attachment, capacity, and aggregate consistent with the tail to be transferred.
Benefits and cash flows
- 1The cedent retains the per-event attachment.
- 2The reinsurer pays excess loss up to layer capacity.
- 3Loss above exhaustion returns to the cedent.
Assumptions
| Assumption | Value / unit | Source and status |
|---|---|---|
| Layer | $80M xs $20M | Illustrative Illustrative 2026 contract |
| Aggregate limit | Capacity × reinstatements | Convention Implemented contract convention |
| Reinstatement premium | Pro rata as to amount | Convention Declared simplification |
Method
Excess of loss
The identity applies per occurrence and then against remaining aggregate capacity.
Recuperación = min(max(0, S − prioridad), capacidad)Results and interpretation
The layer protects the contracted interval; it removes neither the lower retention nor loss above exhaustion.
Applied example
A catastrophe layer, $80M xs $20M
An insurer exposed to hurricanes buys an excess-of-loss layer of $80 million in excess of $20 million. In each event it retains the priority and recovers the excess from the reinsurer, up to the layer's capacity.
Adjust the parameters to observe how the result changes.
Actuarial interpretation
The reinsurer's recovery equals min(max(0, S − priority), capacity). For losses above $100 million the layer is exhausted and the excess reverts to the cedent; in practice this is covered with additional layers or facultative reinsurance.
Validation and limits
What is checked
- —Canonical hand-calculated layers: 5 xs 5, 5 xs 10, and 10 xs 20.
- —Aggregate erosion and reinstatement tests.
What it does not prove
- —Reinstatement proration considers neither time nor tiered rates.
- —What counts as net result changes from treaty to treaty; the difference is recorded in the inventory.