[i_am_proteus]

It might not be positive expected value (dollars) but it's often positive expected utility.

This is usually because insurance hedges against tail risks that wipe out the individual, and in these cases utility is a nonlinear function of dollars.

Most people would rather pay 1% of their net worth to deterministically avoid a 1/100 chance of losing their entire net worth.

Because insurers pool risk, it ends up being simultaneously rational for the individual to carry insurance and profitable for the insurer to write insurance policies.

Investments are a similar kind of risk pooling, but for upsides. You would not gamble your entire net worth on a prospect with uncertain profitability, but a large number of investors each risking a small fraction of their wealth make it possible to raise capital for risky but possibly valuable projects.

[lmohseni]

I like to think of it as: insurance = risk pooling = “socialism”, whereas markets = information pooling = “capitalism”, and risk is simply the negative of information.