Axiomatic Utility Theory under Risk Non-Archimedean Representations
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.
- PDF / 14,259,490 Bytes
- 216 Pages / 439.37 x 666.14 pts Page_size
- 24 Downloads / 206 Views
461
Springer-Verlag Berlin Heidelberg GmbH
Ulrich Schmidt
Axiomatic Utility Theory underRisk Non-Archimedean Representations and Application to Insurance Economics
Springer
Author Dr. Ulrich Schmidt University of Kiel Institut fUr Finanzwissenschaft und Sozialpolitik OlshausenstraBe 40 D-24098 Kiel, Germany
library of Congress Cataloging-in-Publication Data
Schmidt. Ulrlch. 1968Axiomatic uti 1 ity theory under risk nan-archlmedean representations and applicatian ta insurance ecanamics I Ulrich Schmldt. p. cm. -- (Lecture notes In economlCS and mathematical systems ; 461) Thesis (Ph.D. )--Christian-Albrechts-Universitat. 1997. Includes bibl iographical references and Index. ISBN 978-3-540-64319-7 ISBN 978-3-642-58877-8 (eBook) DOI 10.1007/978-3-642-58877-8
1. Uti 1 ity theory. 2. Risk management--Mathematical madels: 3. Insurance--Mathematical models. 1. Title. II. Series. HB201.S415 1998 658.4·03--dc21 98-13678 CIP
ISSN 0075-8442 ISBN 978-3-540-64319-7 This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concemed, specifically the rights of translation, reprinting, re-use of ilIustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use mu~t always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1998
Originally published by Springer-Verlag Berlin Heidelberg New York 1998 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera ready by author SPIN: 10649610 42/3143-543210 - Printed on acid-free paper
To Paula
Preface 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 argument and particularly his choice of a logarithmic utility function 2 seem to be rather arbitrary since they are based entirely on intuitively appealing examples. 3 Not until two centuries later, did von Neumann and Morgenstern (1947) prove that if the preferences of the decision maker satisfy certain assumptions they can be represented by the expected value of a real-valued utility fu
Data Loading...
