Insurance works on a statistical property rather than on prediction. Individual losses are unpredictable, but the total across a large group is stable enough to price.
Aggregation makes the unpredictable predictable
A single household cannot know whether it will suffer a fire this year. Across a large number of similar households, the proportion suffering one is remarkably consistent.
The insurer is not forecasting individual events. It is estimating a rate across a population, which is a much easier problem.
This is why insurers need scale. A small pool produces volatile results even when the underlying rate is well understood.
Independence is the critical assumption
Pooling works when losses are largely unrelated to each other. One house burning does not make the next more likely, so events offset within the pool.
Correlated risks break this. A flood, a windstorm or an earthquake produces many claims simultaneously, and the pool cannot absorb them from that year's premiums.
Insurers manage correlation by limiting concentration in any single area and by transferring the peak exposure to reinsurers who pool across regions.
Premium is more than expected loss
The technical price starts with the expected cost of claims for that risk class. Onto that go administration, claims handling, distribution and the cost of holding capital.
Capital is required because actual claims exceed expectation in some years, and the insurer must be able to pay regardless. Holding it has a cost that policyholders fund.
Investment income on premiums held before claims are paid offsets part of this, which is why insurer profitability is sensitive to interest rates.
Classification is what makes pricing fair
Charging everyone the same would mean low-risk policyholders subsidising high-risk ones, which encourages the low-risk group to leave. The remaining pool then costs more.
Grouping similar risks together keeps prices aligned with expected cost within each group and prevents that unravelling.
Which factors may be used for classification is constrained by regulation, and those constraints differ by jurisdiction and by line of business.
Why some cover is unavailable at any price
Where losses are near certain, insurance ceases to be a transfer of uncertainty and becomes prepayment of a known cost plus expenses.
Where a single event could exhaust the pool, the insurer cannot hold enough capital to write it at a price anyone would pay.
Both cases explain gaps in availability better than reluctance does. The mechanism has conditions, and it stops working when they fail.