An insurer cannot predict whether any particular policyholder will claim. It can predict, with reasonable accuracy, how many of a large group will, and that difference is the entire business.
Aggregation converts uncertainty into a forecast
A single house has either a fire or no fire, which is a highly uncertain outcome. Across many thousands of houses, the proportion experiencing a fire is stable year to year.
Premiums are set against that predictable aggregate rather than against any individual's likelihood of claiming, which no one can know.
Larger pools produce tighter forecasts, which is why scale reduces the margin an insurer must hold and allows premiums to fall.
The pool only works if risks are independent
The stabilising effect depends on losses being unrelated to one another. One house burning does not make the next more likely.
Where exposures are correlated, that assumption fails. A flood, storm or earthquake causes many claims simultaneously from a single event.
Insurers manage this by limiting how much exposure they accept in any one location or peril, which is why coverage can become unavailable in concentrated risk areas.
Premiums fund claims, expenses and capital
The premium covers expected claims, the cost of running the business, and a return on the capital held to absorb years worse than expected.
Investment income on premiums held between collection and payment reduces what must be charged, which links pricing to prevailing interest rates.
Insurers can therefore price more competitively when investment returns are strong, and must raise rates when they are not, independent of claims experience.
Classification decides who shares which pool
Rather than one pool, insurers construct many, grouping policyholders by characteristics associated with different loss frequencies.
Sorting more finely makes each group more homogeneous and prices more accurately, but it also reduces the cross-subsidy that made cover affordable for higher-risk groups.
Regulation limits which characteristics may be used, which is a deliberate decision to preserve some pooling that pure classification would eliminate.
Adverse selection erodes the pool from within
If those most likely to claim are most likely to buy, the pool's loss experience exceeds what the premium assumed.
Rising premiums then drive out the lowest-risk members first, worsening the remaining mix and requiring further increases.
Underwriting questions, waiting periods and exclusions exist to interrupt that spiral, and mandatory participation is the other mechanism used where it cannot be interrupted otherwise.