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The expected utility theory takes into account that individuals may be risk-averse, meaning that the individual would refuse a fair gamble (a fair gamble has an expected value of zero). Risk aversion implies that their utility functions are concave and show diminishing marginal wealth utility.
Expected Utility Theory (EUT) poses a utility calculation linearly combining weights and values of the probabilities associated with various outcomes. By presuming that decision-makers themselves incorporate an accurate weighting of probabilities into calculating expected values for their decision-making, EUT assumes that people's subjective probability-weighting matches objective probability ...
Hyperbolic absolute risk aversion (HARA) is the most general class of utility functions that are usually used in practice (specifically, CRRA (constant relative risk aversion, see below), CARA (constant absolute risk aversion), and quadratic utility all exhibit HARA and are often used because of their mathematical tractability).
In decision theory, the von Neumann–Morgenstern (VNM) utility theorem demonstrates that rational choice under uncertainty involves making decisions that take the form of maximizing the expected value of some cardinal utility function. This function is known as the von Neumann–Morgenstern utility function.
The more special case of the isoelastic utility function, with constant relative risk aversion, occurs if, further, b = 0. The logarithmic utility function occurs for = as goes to 0. The more special case of constant relative risk aversion equal to one — U(W) = log(W) — occurs if, further, b = 0.
The utility function is convex for a risk-lover and concave for a risk-averse person (and subsequently linear for a risk-neutral person). [1] Subsequently, it can be understood that the utility function curves in this way depending on the individual's personal preference towards risk. [1]
In decision theory, the Ellsberg paradox (or Ellsberg's paradox) is a paradox in which people's decisions are inconsistent with subjective expected utility theory. John Maynard Keynes published a version of the paradox in 1921. [1] Daniel Ellsberg popularized the paradox in his 1961 paper, "Risk, Ambiguity, and the Savage Axioms". [2]
Generally, the simplest way to think of the risk-utility test is the Hand Formula applied to products. The Third Restatement of the Law, Torts: Products Liability §2(b) [ 1 ] favors the risk-utility test over the Second Restatement of the Law, Torts §402(a), which favored the consumer expectations test . §2(b) states, in part, "A product is ...