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Nicolaus Bernoulli described the St. Petersburg paradox (involving infinite expected values) in 1713, prompting two Swiss mathematicians to develop expected utility theory as a solution. Bernoulli's paper was the first formalization of marginal utility, which has broad application in economics in addition to expected utility theory. He used ...
The classical resolution of the paradox involved the explicit introduction of a utility function, an expected utility hypothesis, and the presumption of diminishing marginal utility of money. According to Daniel Bernoulli: The determination of the value of an item must not be based on the price, but rather on the utility it yields ...
Bernoulli's imaginary logarithmic utility function and Gabriel Cramer's U = W 1/2 function were conceived at the time not for a theory of demand but to solve the St. Petersburg's game. Bernoulli assumed that "a poor man generally obtains more utility than a rich man from an equal gain" [ 3 ] an approach that is more profound than the simple ...
For instance, expected-utility theory was proposed in 1738 by Daniel Bernoulli [3] as a way of modeling behavior which is inconsistent with expected-value maximization. In 1956, John Kelly devised the Kelly criterion by optimizing the use of available information, and Leo Breiman later noted that this is equivalent to optimizing time-average ...
In 1738, Daniel Bernoulli published a treatise [7] in which he posits that rational behavior can be described as maximizing the expectation of a function u, which in particular need not be monetary-valued, thus accounting for risk aversion. This is the expected utility hypothesis. As stated, the hypothesis may appear to be a bold claim.
In this case, the expected utility of Lottery A is 14.4 (= .90(16) + .10(12)) and the expected utility of Lottery B is 14 (= .50(16) + .50(12)) [clarification needed], so the person would prefer Lottery A. Expected utility theory implies that the same utilities could be used to predict the person's behavior in all possible lotteries. If, for ...
Bernoulli normalizes the expected value by assuming that p i are the probabilities of all the disjoint outcomes of the value, hence implying that p 0 + p 1 + ... + p n = 1. Another key theory developed in this part is the probability of achieving at least a certain number of successes from a number of binary events, today named Bernoulli trials ...
Daniel was the son of Johann Bernoulli (one of the early developers of calculus) and a nephew of Jacob Bernoulli (an early researcher in probability theory and the discoverer of the mathematical constant e). [6] He had two brothers, Niklaus and Johann II. Daniel Bernoulli was described by W. W. Rouse Ball as "by far the ablest of the younger ...