If you have 10% chance to lose -$91 and 90% chance to get +$10, the expected value in money is -$0.1. It sounds bad.
But the relationship between utility and money isn't linear. If for you, $10 is worth 10u and $91 is worth only 89u, this deal has expected value of +0.1u.
Why and how isn't it linear? It's a hard problem that can't be answered easily. However we know it's true for most big institutions in stock and bond markets. A financial product will need to provide extra expected value in term of money to compensate the risk, otherwise no one buys it.
In the real world it always goes the other way--the next dollar is never worth as much as the previous dollar, thus any fair bet costs more (the previous dollar) than it gains (the next dollar.)
That's why you should only engage in negative bets, aka insurance. There you are trading a next dollar (worth less) for a previous dollar (worth more).
This has really made insurance click for me because while I understand it intuitively, I wanted a more scientific foundation to understand its value.
I think a great illustration is an extreme case. If I have a house and just enough income to cover all my needs and wants (including retirement savings), then depending on my attitude an extra $1000 per year might have no effect at all - I have nothing I want to spend it on and nothing to save for.
But losing my home would still be devastating. So the utility value of the $1000 per year for the rest of my life is low or none, but the utility value of the previously earned money I would lose from losing my house is high.
But the relationship between utility and money isn't linear. If for you, $10 is worth 10u and $91 is worth only 89u, this deal has expected value of +0.1u.
Why and how isn't it linear? It's a hard problem that can't be answered easily. However we know it's true for most big institutions in stock and bond markets. A financial product will need to provide extra expected value in term of money to compensate the risk, otherwise no one buys it.