Many different definitions of risk, uncertainty, and ambiguity can be found in the literature. This entry follows the notion commonly used in modern decision theory, e.g. employed by Tversky and Kahneman (1992) and much earlier proposed by Knight (1921). Camerer and Weber (1992) provide a review of various definitions and formalizations.

A decision is called risky when the probabilities that certain states will occur in the future are precisely known, e.g. in a fair roulette game. In contrast, a decision is called uncertain when the probabilities are not precisely known. Examples are the outcomes of sports events, elections or most real investments. Decisions under risk can be seen as a special case of decisions under uncertainty with precisely known probabilities. Risk and uncertainty can be distinguished by the degree with which probabilities are known. In case of uncertainty, probabilities are not precisely known but people can form more or less vage beliefs about probabilities. If people are definitely not able to form any beliefs about probabilities, this special case is termed complete ignorance. The above notion of uncertainty corresponds to the widely used term ambiguity.