Axiomatic Utility Theory under Risk

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Beschreibung

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.

Über den Autor

Professor Dr. Ulrich Schmidt studierte Physik und promovierte zum Dr. rer. nat. Während und nach dieser Zeit arbeitete er in verschiedenen Medienbereichen. Er war bis 2021 Professor für Ton- und Videotechnik am Fachbereich Medientechnik an der Hochschule für angewandte Wissenschaften in Hamburg.

Zusammenfassung

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

Inhaltsverzeichnis

1 A Survey.- 1.1 Introduction.- 1.2 The General Framework.- 1.3 Expected Utility Theory.- 1.4 Generalizations of Expected Utility.- 1.5 Conclusions.- 2 Non-Archimedean Representations.- 2.1 Introduction.- 2.2 Lexicographic Expected Utility.- 2.3 Expected Utility with Certainty Preference.- 2.4 Expected Utility on Restricted Sets.- 2.5 Conclusions.- 3 Application to Insurance Economics.- 3.1 Introduction.- 3.2 Two-Outcome Diagrams.- 3.3 Demand for Coinsurance.- 3.4 Bilateral Risk Sharing.- 3.5 Agency Theory.- 3.6 Conclusions.- References.- List of Symbols.- List of Abbreviations.- List of Figures.

Details

Erscheinungsjahr:	1998
Fachbereich:	Allgemeines
Genre:	Recht , Sozialwissenschaften , Wirtschaft
Rubrik:	Recht & Wirtschaft
Medium:	Taschenbuch
Reihe:	Lecture Notes in Economics and Mathematical Systems
Inhalt:	xv 228 S.
ISBN-13:	9783540643197
ISBN-10:	3540643192
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Schmidt, Ulrich
Hersteller:	Springer Lecture Notes in Economics and Mathematical Systems
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 13 mm
Von/Mit:	Ulrich Schmidt
Erscheinungsdatum:	20.05.1998
Gewicht:	0,353 kg