Reinsurance as a Loss Transformation
Translate treaty wording into gross, ceded, and retained random variables before pricing or capital analysis.
Reinsurance as a Loss Transformation
Reinsurance does not remove uncertainty; it reallocates specified losses. For every outcome,
subject to contract terms, exclusions, reinstatements, expenses, credit risk, and timing.
Contract-first workflow
- Define loss: ground-up, policy payment, event loss, or annual aggregate.
- Define unit: risk, claim, occurrence, policy, or treaty year.
- Apply underlying terms: deductibles, policy limits, exclusions.
- Apply treaty: share, attachment, limit, aggregate deductible, and order.
- Aggregate consistently: recognise claims belonging to the same occurrence.
- Add economics: premium, commission, reinstatement premium, expenses, timing, and counterparty risk.
- Test scenarios: inflation, event clustering, exhaustion, and wording ambiguity.
“£20m excess of £10m” is incomplete until the loss unit and basis are known. The same numbers produce different recoveries per risk, per occurrence, and in annual aggregate.
Treaty map
| Treaty | Core transformation | Responds most directly to |
|---|---|---|
| Quota share | fixed proportion of every covered loss | capital/volume sharing across the portfolio |
| Surplus share | share varies with retained sum insured | heterogeneous policy limits |
| Per-risk excess | layer applied to one insured risk | one large risk loss |
| Per-occurrence excess | layer applied to event aggregation | catastrophe/event accumulation |
| Aggregate excess/stop loss | layer applied to annual total | adverse annual frequency and severity |
Layer notation used in this course
For attachment and limit , ceded loss from input is
“£20m xs £10m” means m and m: the reinsurer pays losses in the layer from £10m to £30m, before other wording effects.
| Input loss | Ceded | Retained |
|---|---|---|
| £6m | £0m | £6m |
| £18m | £8m | £10m |
| £45m | £20m | £25m |
The insurer retains loss below attachment and above exhaustion.
What “better” means
A treaty can be compared on:
- expected ceded loss and expected net result;
- volatility and tail reduction at the chosen horizon;
- probability of attachment and exhaustion;
- liquidity and timing of recoveries;
- basis, credit, legal, and operational risk;
- premium and opportunity cost.
A lower retained 99% quantile is not automatically good value; price and counterparty terms matter.
Proceed from proportional sharing to excess layers, then study inflation and layer erosion and run the treaty comparison lab.