> Insurance premiums are determined by total cost of claims plus expected inflation plus administration costs. There is no "expected cost". You are making this term up.

I'm not using jargon, but the meaning is both clear and correct.

>There is only risk

and the cost of that risk is the meaning of "expected cost".

However, you did make an error. Premiums don't depend on the total cost of claims, but on the EXPECTED total cost of claims. That's where actuaries come in - they predict claims costs (and try to reduce them) - you don't need actuaries to compute the total cost of claims. See if you can figure out why it is the expected and not actual costs.

However, that's just how you get the total payments required to create and maintain a shared-risk pool - you have choices wrt the price paid by different members of the pool. (Actually, it's a shared-cost pool because it's not the incidence odds but the product of the incidence odds and their cost, but I digress.)

Subsidy refers to a class of pricing decisions, namely those that ignore (to some extent) relative costs, so it's neither surprising nor relevant to say that actuaries don't define subsidy. Moreover, actuaries don't determine pricing systems - they merely provide cost-predictions when and where necessary.

For example, you could charge each member their individual predicted claims plus a share of the other costs. This would be risk-based, or rather, expected-cost-based, pricing and is what is traditionally known as "insurance". In this case, actuaries are involved in determining pool-member pricing.

Or, you could charge every member the same amount, namely the total divided by the number of members, even though your actuaries tell you that some members of the pool have higher predicted claims than others. If you do this, the high-expected-cost members of the pool are being subsidized by the low-expected-cost members. This is a subsidy, even though there's still a shared-cost pool. In this case, actuaries have no role in determining a given member's price - they're just needed to determine the expected cost of the whole pool.

Note that high-expected-cost members can save money by leaving a pool that has cost-based pricing for a pool where they'll receive subsidies. However, low-expected-cost members can save money by leaving a pool that requires them to pay subsidies for pool that has cost-based pricing.

In the (artificial) case where all high cost members are identical as are low-cost members, the end result is that everyone ends up paying cost-based prices but they end up in different pools (assuming each pool pays its costs).

>> My risk of having a car accident does not depend on how many people
>> are in "the pool".

>You're failing again to understand the math.

Not at all. You claimed that my risks depended on pool size - they don't. The fact that the variance in total pool claims does depend on pool size doesn't change that fact.

> This is why you can't get insurance if you get sick

Actually, you can. A pool with expected-cost-based pricing makes money on all possible pool members, regardless of expected cost.

However, a pool with subsidies does benefit from avoiding high-expected-cost members.

>There is no real distinction here except for the doublespeak you're introducing in an attempt to somehow differentiate health insurance from any number of insurance services.

I've never tried to differentiate health insurance from other insurance. I'm differentiating different pricing policies for shared-risk pools. Some are insurance while others have internal subsidies.