Skip to main content
SpringerLink
Log in

Axiomatic Utility Theory under Risk

Non-Archimedean Representations and Application to Insurance Economics

  • Book
  • © 1998

Overview

Authors:
  1. Ulrich Schmidt

    1. University of Kiel, Institut für Finanzwissenschaft und Sozialpolitik, Kiel, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Overview on the development of axiomatic utility theory under risk since von Neumann and Morgenstein.
  • New approaches in this field, with important consequences on insurance economics

Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 461)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (3 chapters)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. A Survey

    • Ulrich Schmidt
    Pages 1-67

  3. Non-Archimedean Representations

    • Ulrich Schmidt
    Pages 69-121

  4. Application to Insurance Economics

    • Ulrich Schmidt
    Pages 123-161

  5. Back Matter

    Pages 163-201
    Download chapter PDF
Back to top

Keywords

About this book

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 cer­ 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.

Authors and Affiliations

  • University of Kiel, Institut für Finanzwissenschaft und Sozialpolitik, Kiel, Germany

    Ulrich Schmidt

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation