Shafer Glenn, Vovk Vladimir - Probability and Finance - It's only a game.pdf

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Probability and
Finance
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WILEY SERIES IN PROBABILITY AND STATISTICS
FINANCIAL ENGINEERING SECTION
Established by WALTER A. SHEWHART and SAMUEL S. WILKS
Editors: Peter Bloorqfield, Noel A. C. Cressie, Nicholas 1. Fisher;
Iuin M. John.stone, J. B. Kudane, Louise M. Ryan, David W Scott,
Revnuid
PY Silverman, Adrian E M. Smith, Jozef L. Teugels;
Vic Burnett. Emeritus, Ralph A. Bradley, Emeritirs,
J. Stztul-t Hiinter; Emeritus, David G. Kenclall, Emel-itits
A complete list of the titles in this series appears at the end of this volume.
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Probability and
Finance
It’s Only a Game!
GLENN SHAFER
Rzitgers University
Newark, New Jersey
VLADIMIR VOVK
Rqval Holloway, University of London
Egharn, Surrey, England
A Wiley-Interscience Publication
JOHN WILEY & SONS, INC.
NewYork Chichester Weinheim Brisbane Singapore Toronto
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This text is pi-inted on acid-free paper. @
Copyright C 2001 by John Wiley & Sons. Inc
All rights reserved. Published simultaneously in Canada.
No part of this publication may be reproduced. stored in a retrieval system or transmitted in any
form or by any means, electronic, mechanical. photocopying. recording, scanning or othenvise.
except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without
either the prior written pemiission of the Publisher, or authorization through payment of the
appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA
01923. (978) 750-8400. fax (978) 750-4744. Requests to the Publisher for pelmission should be
addressed to the Permissions Department, John Wiley & Sons, Inc.. 605 Third Avenue, New York,
NY 10158-0012. (212) 850-601 1. fax (212) 850-6008, E-Mail: PERMKEQ @! WILEY.COM.
For ordering and customer service. call I-800-CALL WILEY.
Library of Congress Catulojiing-iit-PNblicution Data:
Shafer, Glenn. I946
Probability and finance : it's only a game! /Glenn Shafer and Vladimir Vovk
p. cin. ~ (Wiley series in probability and statistics. Financial engineering section)
Includes bibliographical references and index.
ISBN 0-471-40226-5 (acid-free paper)
1. Investments-Mathematics.
2. Statistical decision. 3. Financial engineering. 1. Vovk,
Vladimir, 1960-. 11. Title. 111. Series.
HG4S 15 3 .SS34 2001
332'.01'1 -dc21
2001024030
Printed in the United States of America
10987654321
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Contents
Preface
ix
1 Probability and Finance as a Game
1.1 A Game with the World
1.2 The Protocol for a Probability Game
1.3 The Fundamental Interpretative Hypothesis
1.4 The Many Interpretations of Probability
1.5 Game-Theoretic Probability in Finance
1
4
9
14
19
22
Part I Probability without Measure
27
2 The Historical Context
2.1 Probability before Kolmogorov
2.2 Kolmogorov 's Measure-Theoretic Framework
2.3 Realized Randomness
2.4 What is a Martingale?
2.5
2.6 Neosubjectivism
2.7 Conclusion
29
30
39
46
51
55
59
60
V
The Impossibility of a Gambling System
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