Optimal Stopping Problem and Investment Models
The paper is devoted to the description of an approach to solving an optimal stopping problems for multidimensional diffusion processes. This approach is based on connection between boundary problem for diffusion processes and Dirichlet problem for PDE of
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Springer-Verlag Berlin Heidelberg GmbH
Kurt Marti Yuri Ermoliev Georg Pflug (Eds.)
Dynamic Stochastic Optimization
Springer
Editors Prof. Dr. Kurt Marti Federal Armed Forces University Munich Aero-Space Engineering and Technology 85577 NeubiberglMunich, Germany
Prof. Dr. Georg Pflug Institute of Statistics and Decision Support Systems (lSDS) University of Wien 1010 Wien, Austria
Prof. Dr. Yuri Ermoliev IIASA Laxenburg Schlossplatz 1 2361 LaxenburglWien, Austria Cataloging-in-Publication Data applied for A catalog record for this book is available from the Library of Congress. Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
ISBN 978-3-540-40506-1 ISBN 978-3-642-55884-9 (eBook) DOI 10.1007/978-3-642-55884-9 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concemed, specifically the rights of translation, reprinting, re-use of illustrations, 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 ofthe German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law.
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Preface
Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explicitly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objective or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of decision and random variables, and consequently the focus of attention is directed to efficient solution procedures rather than to (analytical) closed-form solutions. Objective and constr
