“expected utility”的概念、定义、翻译、参考文献-科学参考

expected utility

Mathematics

In a context where the outcomes are not determined solely by the decisions an individual takes, the expected utility of a decision is the average value of the utility function weighted by the probability distribution attached to the possible outcomes of the decision.

Philosophy

In decision theory, the expected utility of an outcome is the utility that is assigned to its occurrence, multiplied by the probability of its occurrence. The central concept was first formulated by Christian Huygens (1629–95).

Economics

The expected value of utility from entering a risky prospect. Assume the risky prospect has n potential outcomes. Let the probability of outcome i occurring be p_i and the pay-off if i occurs be X_i. If the utility derived from pay-off X is U(X), then expected utility is

$E [U] = p_{1} U (X_{1}) + … + p_{n} U (X_{n}) .$

The expected utility theorem states that if a consumer satisfies a set of axioms describing rationality they should act in risky situations as if they maximize expected utility. If utility is a linear function of X, then E[U] = U[E(X_i)], that is, expected utility is the utility of the expected value of the pay-offs. If utility is a concave function of pay-off, that is, d²U/dX² < 0, then the expected utility of a risky prospect is less than the utility of the expected pay-off, E[U] < U[E(X_i)], so the consumer prefers a sure pay-off to a risky prospect of the same expected value. See also Allais paradox.

单词	expected utility
释义	expected utility Mathematics In a context where the outcomes are not determined solely by the decisions an individual takes, the expected utility of a decision is the average value of the utility function weighted by the probability distribution attached to the possible outcomes of the decision. Philosophy In decision theory, the expected utility of an outcome is the utility that is assigned to its occurrence, multiplied by the probability of its occurrence. The central concept was first formulated by Christian Huygens (1629–95). Economics The expected value of utility from entering a risky prospect. Assume the risky prospect has n potential outcomes. Let the probability of outcome i occurring be p_i and the pay-off if i occurs be X_i. If the utility derived from pay-off X is U(X), then expected utility is $E [U] = p_{1} U (X_{1}) + … + p_{n} U (X_{n}) .$ The expected utility theorem states that if a consumer satisfies a set of axioms describing rationality they should act in risky situations as if they maximize expected utility. If utility is a linear function of X, then E[U] = U[E(X_i)], that is, expected utility is the utility of the expected value of the pay-offs. If utility is a concave function of pay-off, that is, d²U/dX² < 0, then the expected utility of a risky prospect is less than the utility of the expected pay-off, E[U] < U[E(X_i)], so the consumer prefers a sure pay-off to a risky prospect of the same expected value. See also Allais paradox.
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