Risk aversion

Risk aversion is a preference for a certain outcome over a risky outcome with the same expected value. It is represented in expected utility theory by a concave utility function.

Expected utility theory: A theory of choice that evaluates uncertain prospects by the probability-weighted utility of their outcomes. It models risk aversion as a consequence of diminishing marginal utility.
Expected value: The probability-weighted average of the possible values of a random variable. The comparison holds this quantity equal between the sure and risky outcomes.
Risk neutrality: A preference pattern in which choices depend on expected value rather than uncertainty itself. Unlike a risk-averse chooser, a risk-neutral chooser is indifferent between a sure mean and a fair gamble.
Insurance: A contract that transfers specified financial risks in exchange for premiums. A risk-averse policyholder may pay more than expected loss to replace uncertain costs with a guarantee.
Constant relative risk aversion: A utility specification in which relative risk aversion remains constant as wealth changes proportionally. It is widely used in models, but its assumptions may not fit observed choices across wealth levels.
Utility function: A function that assigns a numerical value to outcomes to represent preferences. Its shape determines whether a decision-maker favors certainty over an equal-expected-value gamble.
Probability distribution: A mathematical description of the possible values of a variable and their probabilities. Risky prospects are distinguished by the distributions of their outcomes.
Risk seeking: A preference for a risky prospect over a sure outcome with the same expected value. It reverses risk aversion and is associated with convex utility over the relevant outcomes.
Portfolio theory: The study of selecting asset combinations to balance expected returns and risk. Risk aversion determines how investors trade portfolio uncertainty against expected return.
Loss aversion: A tendency for losses to have greater psychological impact than equivalent gains. It can make observed risk choices depend on reference points, beyond ordinary concavity.

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