Mathematical Control Theory and Finance
This book highlights recent developments in mathematical control theory and its applications to finance. It presents a collection of original contributions by distinguished scholars, addressing a large spectrum of problems and techniques. Control th
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Andrey Sarychev Albert Shiryaev Manuel Guerra Maria do Rosário á Grossinho Editors ●
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Mathematical Control Theory and Finance
Prof. Andrey Sarychev DiMaD University of Florence via Cesare Lombroso, 6/17 50134 - Florence Italy [email protected]
Prof. Albert Shiryaev Steklov Mathematical Institute of the Russian Academy of Sciences Gubkin str. 8 119991 Moscow Russia [email protected]
Dr. Manuel Guerra ISEG-TU Lisbon Rua do Quelhas, 6 1200-781 Lisbon Portugal [email protected]
Dr. Maria do Rosário Grossinho ISEG-TU Lisbon Rua do Quelhas, 6 1200-781 Lisbon Portugal [email protected]
ISBN 978-3-540-69531-8
e-ISBN 978-3-540-69532-5
Library of Congress Control Number: 2008929628 © 2008 Springer-Verlag Berlin Heidelberg 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 permissions for use must always be obtained from Springer-Verlag. Violations are liable for 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: WMXDesign GmbH, Heidelberg, Germany Printed on acid-free paper 987654321 springer.com
Preface
Control theory provides a large set of theoretical and computational tools with applications in a wide range of fields, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to find solutions to ”real life” problems, as is the case in robotics, control of industrial processes or finance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the financial analyst to possess a high level of mathematical skills. Conversely, the complex challenges posed by the problems and models relevant to finance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical finance. Up to now, other branches of control theory have found comparatively less application in financial problems. To some extent, deterministic and stochastic control theories developed as different branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these fields has intensified. Some concepts from stochastic calculus (e.g., rough paths) have drawn th
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