Definition
Risk aversion is the tendency to prefer a certain outcome to a gamble of the same expected value. A risk-averse person would rather receive a guaranteed $50 than face a 50/50 chance of $0 or $100, even though both have the same expected value of $50.
Formally, risk aversion corresponds to a concave utility function: the marginal utility of money decreases as wealth grows. Risk aversion explains why insurance markets exist, why people diversify their portfolios, and why expected-value maximisation alone is a poor description of real choices.
Why it matters
How it works
To model risk aversion mathematically, replace expected value with expected utility: weight each outcome by its probability and by a utility function u(x), then choose the option with the highest expected utility. If u is concave (curves downward), the agent prefers certainty to variability, all else equal.
The certainty equivalent is the guaranteed amount that an agent would accept in exchange for a gamble. The gap between expected value and certainty equivalent is the risk premium — what the agent is willing to pay to remove the uncertainty. Insurance pricing is essentially a market for risk premia.