Markov Decision Processes with Applications to Finance
The theory of Markov decision processes focuses on controlled Markov chains in discrete time. The authors establish the theory for general state and action spaces and at the same time show its application by means of numerous examples, mostly taken from t
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Universitext Series Editors: Sheldon Axler San Francisco State University Vincenzo Capasso Università degli Studi di Milano Carles Casacuberta Universitat de Barcelona Angus J. MacIntyre Queen Mary, University of London Kenneth Ribet University of California, Berkeley Claude Sabbah CNRS, École Polytechnique Endre Süli University of Oxford Wojbor A. Woyczynski Case Western Reserve University
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Nicole Bäuerle
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Ulrich Rieder
Markov Decision Processes with Applications to Finance
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Nicole Bäuerle Institute for Stochastics Karlsruhe Institute of Technology 76128 Karlsruhe Germany [email protected]
Ulrich Rieder Institute of Optimization and Operations Research University of Ulm 89069 Ulm Germany [email protected]
ISBN 978-3-642-18323-2 e-ISBN 978-3-642-18324-9 DOI 10.1007/978-3-642-18324-9 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011929506 Mathematics Subject Classification (2010): 90C40, 93E20, 60J05, 91G10, 93E35, 60G40 © Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm 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 must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. 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. Cover design: deblik Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
F¨ ur Rolf, Katja und Hannah. F¨ ur Annika, Alexander und Katharina.
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Preface
Models in mathematical finance, for example stock price processes, are often defined in continuous-time. Hence optimization problems like consumptioninvestment problems lead to stochastic control problems in continuous-time. However, only a few of these problems can be solved explicitly. When numerical methods
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