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Distorted Probabilities and Choice under Risk

  • Book
  • © 1991

Overview

Authors:
  1. Clemens Puppe

    1. Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, Karlsruhe 1, Germany

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Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 363)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Introduction

    • Clemens Puppe
    Pages 1-7

  3. Axiomatic Utility Theory under Risk

    • Clemens Puppe
    Pages 8-39

  4. A Rank-Dependent Utility Model with Prize-Dependent Distortion of Probabilities

    • Clemens Puppe
    Pages 40-66

  5. Risk Aversion

    • Clemens Puppe
    Pages 67-87

  6. Conclusion

    • Clemens Puppe
    Pages 88-91

  7. Back Matter

    Pages 92-104
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Keywords

About this book

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.

Authors and Affiliations

  • Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, Karlsruhe 1, Germany

    Clemens Puppe

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