- Häftad (Paperback / softback)
- Antal sidor
- Softcover reprint of the original 1st ed. 1991
- Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- VIII, 100 p.
- 234 x 156 x 6 mm
- Antal komponenter
- 1 Paperback / softback
- 173 g
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Distorted Probabilities and Choice under Risk729Skickas inom 10-15 vardagar.
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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.
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Fler böcker av Clemens Puppe
Paul Anand, Prasanta Pattanaik, Clemens Puppe
The Handbook of Rational and Social Choice provides an overview of issues arising in work on the foundations of decision theory and social choice over the past three decades. Drawing on work by economic theorists mainly, but also with contribution...
1 Axiomatic Utility Theory under Risk.- 1.1 Historical Overview.- 1.2 The Axiomatic Basis of Expected Utility Theory.- 1.3 The Empirical Evidence against the Independence Axiom.- 1.4 Non-Linear Utility Theory under Risk.- 1.4.1 Weighted Linear Utility Theory.- 1.4.2 Theories with the Betweenness Property.- 1.4.3 Anticipated Utility Theory.- 1.4.4 The Dual Theory.- 1.4.5 The General Rank-Dependent Utility Model.- 1.4.6 Implicit Rank-Linear Utility Theory.- 2 A Rank-Dependent Utility Model with Prize-Dependent Distortion of Probabilities.- 2.1 Rank-Dependent Utility Theory Reconsidered.- 2.1.1 The Generalized Utility Function.- 2.1.2 Absolute Continuity.- 2.1.3 The Set of Elementary Lotteries.- 2.2 Homogeneity on Elementary Lotteries.- 2.2.1 The Common Ratio Effect.- 2.2.2 The Allais Paradox.- 2.3 Further Evidence for Prize-Dependent Distortions of Probabilities.- 2.4 A Characterization Theorem.- 2.5 Rank-Dependent Utility Theory and Relative Utility.- 2.6 A Generalized Model.- 3 Risk Aversion.- 3.1 Risk Aversion in the General Rank-Dependent Utility Model.- 3.2 Risk Aversion and Homogeneity.- 3.3 Decreasing Risk Aversion.- 3.4 The Friedman-Savage Hypothesis.- Conclusion.- References.