Stochastic Dominance Investment Decision Making under Uncertainty
This book is devoted to investment decision-making under uncertainty. The book covers three basic approaches to this process: a) The stochastic dominance approach, developed on the foundation of von Neumann and Morgenstern' expected utility paradigm. 2 b
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Stocbastic Dominance byHaimLevy Myles Robinson Professor ofFinance The Hebrew University of Jerusalem
Previously published books in the series: Viscusi, W. Kip: STUDIES IN RISK AND UNCERTAINTY Luken, R.: ENVIRONMENTAL REGULATION: TECHNOLOGY, AMBIENT AND BENEFITS-BASED APPROACHES Shubik, M.: RISK, ORGANIZATIONS AND SOCIETY Edwards, W.: UTILITY THEORIES: MEASUREMENTS AND APPLICATIONS Martin, W.: ENVIRONMENTAL ECONOMICS AND THE MINING INDUSTRY Kunreuther, H. and Easterling, D.: THE DILEMMA OF A SITING OF HIGH-LEVEL NUCLEAR WASTE REPOSITORY Kniesner, T. and Leeth, J.: SIMULATING WORKPLACE SAFETY POLICY Christe, N.G.S. and Soguel, N.C.: CONTINGENT VALVATION, TRANSPORT SAFETY Battigalli, P., Montesano, A. and Panunzi, F.: DECISIONS, GAMESAND MARKETS Freeman, P. and Kunreuther, H.: MANAGING ENVIRONMENTAL RISK THROUGH INSURANCE Kopp, R.J., Pommerehne, W.W. and Schwartz, N.: DETERMINING THE VALUE OF NON-MARKETED GOODS Bishop, R.C. and Romano, D.: ENVIRONMENTAL RESOURCE VALVATION: APPLICATIONS OF THE CONTINGENT VALUATION METHOD IN ITALY
STOCHASTIC DOMINANCE Investment Decision Making under Uncertainty
by
Haim Levy Myles Robinson Professor of Finance The Hebrew University of Jerusalem
Springer Science+Business Media, LLC
Library of Congress Cataloging-in-Publication Data Stochastic dominance : investment decision making under uncertainty / edited by Haim Levy. p. cm. -- (Studies in risk and uncertainty) Includes bibliographical references and index. ISBN 978-1-4757-2842-2 ISBN 978-1-4757-2840-8 (eBook) DOI 10.1007/978-1-4757-2840-8
1. Investment analysis--Mathematics. 2. Stochastic processes. 3. Statistica) decision. 1. Levy, Haim. II. Series. HG4529.S75 1998 332.6'01 '51--dc21 98-34577 CIP Copyright © 1998 by Springer Science+Business Media New York. Originally published by Kluwer Academic Publishers in 1998 Softcover reprint of the hardcover 1st edition 1998 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, LLC.
Printed on acid-free paper.
To Tal, Shira, Tamar, and Neta
TABLE OF CONTENTS
Preface
I
I On the Measurement of Risk
5
1.1 1.2
1.3
What is Risk? Measures of Risk a) Domar and Musgrave Risk Indexes b) Roy's Safety First Rule c) Dispersion as a Risk Index: Variance and Standard Deviation d) Semi-variance (SV) as an index ofrisk e) Baumol's Risk Measure t) Loss as an Alternative Cost: The Minimax Regret Summary
2 Expected Utility Theory
2.1 2.2 2.3
2.4 2.5 2.6 2.7
Introduction Investment Criteria a) The Maximum Return Criterion (MRC) b) The Maximum Expected Return Criterion (MERC) The Axiomsand Proofofthe Maximum Expected Utility Criterion (MEUC) a) The Payoffofthe Investments b) The Axioms c) Proofthat the Maximum Expected Utility Criterion (MEUC) is Optimal Decision Rule The Properties ofUtility Function a) Preference and Expected Utility b) Is U(x) a Probability Fun
