During the development of modern probability theory in the 17th cen- tury it was commonly held that the attractiveness of a gamble offering the payoffs:1:17 ---: l: with probabilities Pl, . . ., Pn is given by its expected n value L:: l: iPi. Accordingly, the decision problem of choosing among different such gambles - which will be called prospects or lotteries in the sequel-was thought to be solved by maximizing the corresponding expected values. The famous St. Petersburg paradox posed by Nicholas Bernoulli in 1728, however, conclusively demonstrated the fact that individuals l consider more than just the expected value. The resolution of the St. Petersburg paradox was proposed independently by Gabriel Cramer and Nicholas's cousin Daniel Bernoulli [BERNOULLI 1738/1954]. Their argument was that in a gamble with payoffs: l: i the decisive factors are not the payoffs themselves but their subjective values u(: l: i)' According to this argument gambles are evaluated on the basis of the expression L: U(Xi)pi. This hypothesis -with a somewhat different interpretation of the function u - has been given a solid axiomatic foundation in 1944 by v. Neumann and Morgenstern and is now known as the expected utility hypothesis. The resulting model has served for a long time as the preeminent theory of choice under risk, especially in its economic applications.
Series: Lecture Notes in Economic and Mathematical Systems
Number Of Pages: 100
Published: 10th July 1991
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6 x 0.61
Weight (kg): 0.17