apparently to figure out whether the risk is worth taking you multiply expected value of the outcome by it's probability.
Nope, that's how you calculate the expected value and not the risk. In fact, risk is entirely absent from this calculation.
But buying insurance is a slightly different question. Basically, insurance makes sense when a possible loss will have large secondary and tertiary effects the negative value of which is large.
For example, consider a retired couple without much savings living in a house with a paid-off mortgage. Let's say the house is worth $200K. What happens if the house burns down? Is their loss $200K? Nope, their loss is much bigger because they don't have a place to live, can't afford another house, and their life just got much worse -- more than the nominal loss of $200K would indicate.
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)