Ulrich Schmidt's Axiomatic Utility Theory under Risk: Non-Archimedean PDF

By Ulrich Schmidt

ISBN-10: 3540643192

ISBN-13: 9783540643197

ISBN-10: 3642588778

ISBN-13: 9783642588778

The first makes an attempt to increase a software conception for selection occasions less than possibility have been undertaken through Cramer (1728) and Bernoulli (1738). contemplating the recognized St. Petersburg Paradox! - a lottery with an unlimited anticipated financial worth -Bernoulli (1738, p. 209) saw that the majority humans wouldn't spend an important amount of cash to interact in that gamble. To account for this remark, Bernoulli (1738, pp. 199-201) proposed that the predicted financial worth needs to be changed through the predicted software ("moral expectation") because the appropriate criterion for determination making below hazard. despite the fact that, Bernoulli's 2 argument and especially his number of a logarithmic application functionality appear to be really arbitrary given that they're dependent fullyyt on intuitively three beautiful examples. now not until eventually centuries later, did von Neumann and Morgenstern (1947) end up that if the personal tastes of the choice maker fulfill cer­ tain assumptions they are often represented by way of the predicted price of a real-valued application functionality outlined at the set of effects. regardless of the same mathematical type of anticipated application, the idea of von Neumann and Morgenstern and Bernoulli's procedure have, despite the fact that, IFor finished discussions of this paradox cf. Menger (1934), Samuelson (1960), (1977), Shapley (1977a), Aumann (1977), Jorland (1987), and Zabell (1987). 2Cramer (1728, p. 212), nevertheless, proposed that the application of an sum of money is given by way of the sq. root of this amount.

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Additional resources for Axiomatic Utility Theory under Risk: Non-Archimedean Representations and Application to Insurance Economics

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58 Note that some authors distinguish between normative and prescriptive theories. In this study, however, we follow the argument of Howard (1992, pp. 51-52) and use the words normative and prescriptive in the same sense. 59Cf. Keeney (1992, pp. 57-58). 19 Obviously, the results presented in the last section indicate that expected utility does not describe actual choice behavior accurately. Therefore, expected utility is without doubt unsuitable as a descriptive theory for decision making under risk.

77-78). 8 and assume that 9 is strictly concave which is implied by strict risk aversion. 39) immediately implies that indifference curves are steepest in the corner P2 = 1 and are getting flatter as one moves in northern or in eastern direction. 8: Anticipated utility Source: Weber and Camerer (1987, p. 143) Along the hypotenuse all indifference curves have an identical slope (hypotenuse parallelism) since P2 = 0 yields PI = 1 - P3. Thus, indifference curves in anticipated utility theory do not satisfy the fanning out hypothesis.

91Cf. Chew and Nishimura (1992, p. 298). 4 The Theory of Disappointment A version The purpose of the theory of disappointment aversion is to characterize the most restrictive model which can accommodate the common ratio effect and contains expected utility as a special case. 92 As in the preceding section, a consequence x is said to cause disappointment if 8x -< p. 4. Note that r has a lower probability of a disappointing consequence than s since 1 - >. < 1 - /-t. e. ) ... - {q E ps I x E supp(q) =} P )- 8x }.

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Axiomatic Utility Theory under Risk: Non-Archimedean Representations and Application to Insurance Economics by Ulrich Schmidt


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