No, they're not a superset. You can have events with a very low probability and very little variance, events with very low probability and very high probability

No, they're not a superset. You can have events with a very low probability and very little variance, events with very low probability and very high probability, higher probability with low variance, and high probability with very high variance. Here's some random numbers,say for a hypothetical 100,000 hypothetical year long policies low probability, low variance: E(total claims) := 20, V(total claims) := 1 low probability, high variance: E(total claims) := 20, V(total claims) := 20 higher probability, low variance: E(total claims) := 20,000, V(total claims) := 10 higer probability, high variance: E(total claims):= 20,000, V(total claims): 10,000 Premiums don't usually make their way into investing for a bit. They're used to cover claims and then business overheads and then even dividends first. First they go to claims, because there's usually regulations to prevent price gouging that require insurers to refund premium if the ratio of aggregate premium : aggregate claims gets too high (the regulation is on a state by state basis in the US). Then any remainder goes to any other outlay first, so that the invested money can be/stay invested into longer term investments. Only if those outlays can be completely covered by the premium (and i'm skipping over a few things like regulations regarding various levels of liquidity for different risk levels and other stuff) then yeah it can make its way over to the actual investment fund. But in general the business model for insurers is that underwriting profit, limited as it is by regulations, is primarily used for actually running day to day operations and isn't a reliable source for being turned over to the investing side. The investing side is primarily using the initial capitalization of the insurer and the returns from earlier investments. One way of looking at insurance is that the insured is actually buying an option against the insured's capitalization with very limited exercise clauses, but the the insurer pays out exercised options with the money from other purchased options contracts.