Proportional shares everything; non-proportional waits in the wings
The earlier guides in this rung introduced the proportional family — quota share and surplus share — where the reinsurer takes a fixed slice of every premium and pays the same slice of every claim, big or small. That is reinsurance as a silent business partner: it is in on each policy from the first dollar, win or lose. Non-proportional reinsurance works on a completely different principle. The reinsurer collects a premium and then simply *waits*. It pays nothing at all until a loss climbs past an agreed height, and even then it pays only the part that pokes above that line.
The intuition is the same one behind an ordinary policy deductible, just turned upside down for the insurer's own benefit. A household keeps the small, frequent losses itself and insures only the rare large ones; here the *insurer* keeps the small, frequent claims on its own books — the part it can comfortably absorb from premium income — and buys protection only for the catastrophic peaks that would threaten its survival. The technical name for the threshold is the attachment point, and the amount of cover sitting above it is the limit. This is exactly the excess-of-loss design you glimpsed in the ruin-theory rung, now examined up close.
The layer: attachment, limit, and the tower above
A non-proportional cover is described by two numbers and read like a height on a wall. The first is the attachment point — how high a loss must climb before the reinsurer is touched at all. The second is the limit — how much vertical cover sits above the attachment. Reinsurers write it compactly as 'limit excess of attachment', for example '4 million xs 1 million', meaning the reinsurer pays the slice of any loss between 1 million and 5 million. Below 1 million the insurer is on its own; above 5 million the cover is exhausted and the excess falls back on the insurer again unless a higher layer catches it.
Real programmes are rarely a single band. Insurers build a *tower* of stacked layers, each placed end to end up the wall: a working layer just above the retention that gets hit fairly often, then higher layers that respond only to genuine catastrophes. Higher layers cost much less per dollar of cover, because the losses that reach them are far rarer — but when they do hit, they hit hard. Different reinsurers around the world subscribe to different slices of the same tower, which is how a single windstorm in one country ends up shared across dozens of balance sheets on three continents.
Layer: 4,000,000 xs 1,000,000 (limit excess of attachment)
loss = 600,000 -> insurer pays 600,000 ; reinsurer pays 0
loss = 1,000,000 -> insurer pays 1,000,000; reinsurer pays 0
loss = 3,500,000 -> insurer pays 1,000,000; reinsurer pays 2,500,000
loss = 5,000,000 -> insurer pays 1,000,000; reinsurer pays 4,000,000 (limit full)
loss = 9,000,000 -> insurer pays 1,000,000 + 4,000,000 = 5,000,000
reinsurer pays 4,000,000 (capped); 4,000,000 spills above
Reinsurer pays min( max(loss - 1,000,000, 0), 4,000,000 ).Per-risk versus per-occurrence: what counts as one loss?
Everything above hinged on the size of 'a loss' — so the contract must say exactly what one loss *is*. This is where excess-of-loss splits into two flavours. A per-risk treaty applies the attachment and limit to each individual risk separately: one building, one ship, one policy. It protects the insurer against an unusually large single claim — a factory that burns to the ground — and is the natural partner of excess of loss on a book of large, lumpy exposures.
A per-occurrence treaty does something subtler and far more important for catastrophes: it sums up *all* the claims arising from a single event before applying the attachment and limit. A hailstorm might damage ten thousand cars, each a tiny claim that no per-risk cover would ever touch — but added together they are a single catastrophic occurrence, and a per-occurrence layer responds to the total. This is the form that catastrophe excess of loss takes, and it explains why the contract's definition of an 'occurrence' — a single hour clause, a single named storm, a 72-hour window — can be worth hundreds of millions when a hurricane and the flood behind it argue over whether they are one event or two.
Aggregate stop-loss: protecting the whole year
Per-risk and per-occurrence both ask 'how big was that one bad thing?' Stop-loss reinsurance asks an entirely different question: 'how bad was the whole year, added up?' It applies the attachment and limit not to any single loss but to the insurer's *total* claims over the period — the aggregate. The reinsurer pays nothing until the year's accumulated losses pass the attachment, then covers the excess up to the limit. It is the ultimate backstop against a year that goes wrong in a thousand small ways at once: not one giant fire, but a flu season, a soft market, and a run of bad weather all landing together.
Stop-loss is most often quoted as a loss ratio rather than a money amount — for instance, the reinsurer pays losses between 105% and 130% of premium. Below 105% the year was acceptable and the insurer carries it; above 130% the insurer is exposed again. Because it protects the *result* rather than any individual claim, stop-loss is the deal that most directly smooths the bottom line and stabilises the combined-ratio-style profitability the previous rungs taught you to read. It is also, for the same reason, the most expensive and the hardest to buy: a reinsurer covering your entire year's downside has handed you a strong temptation to relax your own underwriting, so these treaties almost always force the insurer to keep meaningful skin in the game.
Reinstatements: bringing exhausted cover back to life
Here is a danger the layer language quietly conceals. Once a catastrophe burns through your '4 million xs 1 million' layer, that cover is *exhausted* — and a single hurricane season can easily deliver a second storm. Without a remedy you would be wholly unprotected for the rest of the year, precisely when nerves are rawest. The reinstatement clause is the remedy: it lets the insurer restore an exhausted layer, often back to its full original limit, so it stands ready for the next event. A treaty might allow one, two, or even unlimited reinstatements, written as part of the original terms.
Reinstatements are not free, and the way they are priced matters. A reinstatement is usually 'paid' — the insurer owes an extra reinstatement premium to switch the cover back on, and that premium is commonly *pro rata to amount* (scaled by how much of the limit was used) and sometimes pro rata to time. So a single large loss can trigger two cash flows in the same direction at once: the reinsurer pays the recovery, and the insurer pays to reload the gun. When you read that a layer cost, say, a 100,000 premium 'with one reinstatement at 100%', it means a second full limit is available but a second full premium falls due if and when the first limit is consumed.
The honest framing is that a reinstatement clause turns a layer from a one-shot shield into a magazine of shots — but a finite, costed one. Pricing the layer therefore means pricing not just the expected recoveries but the expected reinstatement premiums too, and modelling how likely a second or third event is within a single contract year. This is where the loss-distribution and aggregate-modelling skills from earlier in the ladder earn their keep: the value of a reinstatement depends entirely on the chance the limit is exhausted more than once, which is a question about the tail of the frequency distribution, not a clause you can price by intuition alone.
Putting the toolkit together
Non-proportional reinsurance is, at heart, a way of buying down the worst part of a probability distribution and nothing else. You decide which 'worst' you fear most, and you choose the treaty shape that answers it.
- Decide what you fear: a single huge claim (per-risk), a single huge event (per-occurrence), or a single huge year (stop-loss).
- Set the attachment at the level you can comfortably absorb yourself, and the limit high enough to reach the catastrophe you are guarding against.
- Stack layers into a tower if one band is not enough, and add reinstatements where a second event within the year is plausible.
- Price every piece on the loss model — expected recoveries plus expected reinstatement premiums — never on a round number that merely feels safe.
Two honest caveats close the picture. First, non-proportional cover does nothing about the small, frequent losses you keep below the attachment — those are exactly the claims a proportional quota-share treaty is good at sharing, which is why real insurers mix both families rather than choosing one. Second, the protection is only as good as the contract's fine print: the definition of an occurrence, the reinstatement count, the hours clause, and the limit ceiling are not legal trivia but the precise boundaries of what is and is not covered when the worst day finally arrives. The next guides take this same machinery up into catastrophe reinsurance and out to the capital markets, where the same layer-and-limit logic is dressed up as bonds and traded with investors.