Clemens Puppe

Distorted Probabilities and Choice under Risk

• Broschiertes Buch

Produktbeschreibung

This book provides a systematic, formal treatment of a recently proposed extension of the expected utility model of choice under risk: the so-called rank-dependent utility model. In this approach the representation of preferences is based upon a (generalized) utility function defined on the outcome/probability-plane. The main purpose of the book is to demonstrate the flexibility of this model with respect to its explanatory power. This is achieved by analyzing a certain subclass of the rank-dependent utility approach which incorporates the notion of price-dependent distortions of probabilities. This particular approach captures an optimistic point of view towards gambling (as can often be observed), whilst being compatible with a suitably formulated concept of risk aversion. The resulting model is used to explain some of the observed behavioral patterns as the Allais-paradox and the behavior described by the Friedman-Savage hypothesis.

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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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Produktdetails

• Lecture Notes in Economics and Mathematical Systems 363
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-54247-6
• 1991.
• Seitenzahl: 116
• Erscheinungstermin: 10. Juli 1991
• Englisch
• Abmessung: 242mm x 170mm x 7mm
• Gewicht: 176g
• ISBN-13: 9783540542476
• ISBN-10: 3540542477
• Artikelnr.: 09216802

Inhaltsangabe

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.- 2 A Rank-Dependent Utility Model with Prize-Dependent Distortion of Probabilities.- 2.1 Rank-Dependent Utility Theory Reconsidered.- 2.2 Homogeneity on Elementary Lotteries.- 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.