That is really not how the insurance seller's business model works.
Think about it this way: on a given year, they are collecting "Sales" amount of money from their pool of customers. For the insurer to make a profit, the amount reimbursed to legit claims simply has to be less than Sales-Expenses that year, which basically translates to having Z customers claims on any given year where Z << NbOfCustomers.
So it's a bit like a Ponzi scheme, whereby you can benefit as a customer if you pay year 1 and get a claim during year 1 or 2 for example, and the insurer can benefit too if many customers pay "a year in advance" (money that can be invested) before having their claims fall on years 2 or 3 (or never).
The customers can earn investment returns just like the insurance seller, so you have to reduce foregone returns from the insurance buyer’s benefit so it ends up canceling out.
>For the insurer to make a profit, the amount reimbursed to legit claims simply has to be less than Sales-Expenses that year, which basically translates to having Z customers claims on any given year where Z << NbOfCustomers.
That inequality does not “basically translate”. Insurance sellers have to exist for multiple years, not just 1 year.
If every single year, “customer claims” are less than the net benefit of customers, which is what I think you wrote although it is hard to interpret, then your “net benefit of customers” includes a non cash component (such as feeling secure)”.
There is never a free lunch, and the insurance business is not at all like a Ponzi scheme (that’s the whole point of actuaries performing calculations…to ensure sustainability without an ever growing income stream).
Think about it this way: on a given year, they are collecting "Sales" amount of money from their pool of customers. For the insurer to make a profit, the amount reimbursed to legit claims simply has to be less than Sales-Expenses that year, which basically translates to having Z customers claims on any given year where Z << NbOfCustomers.
So it's a bit like a Ponzi scheme, whereby you can benefit as a customer if you pay year 1 and get a claim during year 1 or 2 for example, and the insurer can benefit too if many customers pay "a year in advance" (money that can be invested) before having their claims fall on years 2 or 3 (or never).