Mathematics of Financial Markets
This work is aimed at an audience with asound mathematical background wishing to leam about the rapidly expanding field of mathematical finance. Its content is suitable particularly for graduate students in mathematics who have a background in measure the
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Springer Finance Risk-NeutraI Valuation: Pricing and Hedging of Financial Derivatives N.H. Bingham and Rüdiger Kiesel ISBN 1-85233-001-5 (1998) Visual Exploration in Finance with Self-Organizing Maps Guido Deboeck and Teuvo Kohonen (Editors) ISBN 3-540-76266-3 (1998) Mathematics of Financial Markets Robert J. Elliott and P. Ekkehard Kopp ISBN 0-387-98553-0 (1999) Mathematical Models of Financial Derivatives Y.-K. Kwok ISBN 981-3083-25-5 (1998)
Robert J. Elliott and P. Ekkehard Kopp
Mathematics of Financial Markets
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Springer
Robert J. Elliott Department of Mathematical Sciences University of Alberta Edmonton, Alberta T6G 2G 1 Canada e-mail: [email protected]
P. Ekkehard Kopp Pro-Vice-Chancellors' Office The University of Hull Hull HU6 7RX UK e-mail: [email protected]
Mathematics Subject Classification (1991): 60H30, 90A09 With 6 figures. Library of Congress Cataloging-in-Publication Data Elliott, Robert James. Mathematics of financial markets / Robert J. Elliott, P. Ekkehard Kopp. p. cm. Inc1udes bibliographical references and index. I. Investments-Mathematics. 2. Stochastic analysis. 3. Options (Finance )-Mathematical models. 4. Securities-Prices-Mathematical models. I. Kopp, P.E., 1944. 11. Title. HG4515.3.E37 1998 98-8540 332.6°0I 51-dc21 o
Printed on acid-free paper. © 1999 Springer Science+Business Media New York Originally published by Springer-Verlag New York, Inc in 1999. Softcover reprint of the hardcover 1st edition 1999 All rights reserved. This work may not be translated or copied in whole or in part without the written permission ofthe publisher (Springer Science+Business Media, LLC), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrievaI, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production managed by Francine McNeill; manufacturing supervised by Thomas King. Typeset by The Bartlett Press, Inc., Marietta, GA.
9 8 7 6 5 4 3 2 1 ISBN 978-1-4757-7148-0 ISBN 978-1-4757-7146-6 (eBook) DOI 10.1007/978-1-4757-7146-6
SPIN 10681002
Preface
This work is aimed at an audience with asound mathematical background wishing to leam about the rapidly expanding field of mathematical finance. Its content is suitable particularly for graduate students in mathematics who have a background in measure theory and prob ability. The emphasis throughout is on developing the mathematical concepts required for the theory within the context of their application. No attempt is made to cover the bewildering variety of novel (or 'exotic') financial instruments that now appear on the derivatives markets; the focus
