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Lecture Notes in Economics and Mathematical Systems

Axiomatic Utility Theory under Risk

Non-Archimedean Representations and Application to Insurance Economics

Authors: Schmidt, Ulrich

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The first attempts to develop a utility theory for choice situations under risk were undertaken by Cramer (1728) and Bernoulli (1738). Considering the famous St. Petersburg Paradox! - a lottery with an infinite expected monetary value -Bernoulli (1738, p. 209) observed that most people would not spend a significant amount of money to engage in that gamble. To account for this observation, Bernoulli (1738, pp. 199-201) proposed that the expected monetary value has to be replaced by the expected utility ("moral expectation") as the relevant criterion for decision making under risk. However, Bernoulli's 2 argument and particularly his choice of a logarithmic utility function seem to be rather arbitrary since they are based entirely on intuitively 3 appealing examples. Not until two centuries later, did von Neumann and Morgenstern (1947) prove that if the preferences of the decision maker satisfy cerĀ­ tain assumptions they can be represented by the expected value of a real-valued utility function defined on the set of consequences. Despite the identical mathematical form of expected utility, the theory of von Neumann and Morgenstern and Bernoulli's approach have, however, IFor comprehensive discussions of this paradox cf. Menger (1934), Samuelson (1960), (1977), Shapley (1977a), Aumann (1977), Jorland (1987), and Zabell (1987). 2Cramer (1728, p. 212), on the other hand, proposed that the utility of an amount of money is given by the square root of this amount.

Table of contents (3 chapters)

Table of contents (3 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-642-58877-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-3-540-64319-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Axiomatic Utility Theory under Risk
Book Subtitle
Non-Archimedean Representations and Application to Insurance Economics
Authors
Series Title
Lecture Notes in Economics and Mathematical Systems
Series Volume
461
Copyright
1998
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-58877-8
DOI
10.1007/978-3-642-58877-8
Softcover ISBN
978-3-540-64319-7
Series ISSN
0075-8442
Edition Number
1
Number of Pages
XV, 228
Topics