It can be rational because of diminishing marginal utility (happiness) of money. Imagine if I'm poor I get 100 units of pleasure from having an extra $10,000 whereas if I'm rich I get only 50 units of pleasure from having an extra $10,000. If I face some risk of becoming poor I would be willing to buy insurance that takes money from me in the state in which I'm rich and gives it to me in the state in which I'm poor even if on average I end up losing money, because on average I will end up gaining utility.
Hey, everyone! So I've been reading an article about the expected utility, apparently to figure out whether the risk is worth taking you multiply expected value of the outcome by it's probability.
And apparently insurance companies can make money because the expected utility of buying insurance is lower than it's price.
So why would buying insurance be the rational action? I mean intuitively it makes sense(you want to avoid the risk), but it doesn't seem to fit well with this idea. If insurance is almost by definition is worth slightly less than it's price, how is it worth buying?
(sorry if it's a dumb question)