Convex Duality
We present a concise description of the convex duality theory in this chapter. The goal is to lay a foundation for later application in various financial problems rather than to be comprehensive. We emphasize the role of the subdifferential of the value f
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Peter Carr · Qiji Jim Zhu
Convex Duality and Financial Mathematics
123
SpringerBriefs in Mathematics Series Editors Nicola Bellomo Michele Benzi Palle Jorgensen Tatsien Li Roderick Melnik Otmar Scherzer Benjamin Steinberg Lothar Reichel Yuri Tschinkel George Yin Ping Zhang
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Peter Carr • Qiji Jim Zhu
Convex Duality and Financial Mathematics
123
Peter Carr Department of Finance and Risk Engineering Tandon School of Engineering New York University New York, NY, USA
Qiji Jim Zhu Department of Mathematics Western Michigan University Kalamazoo, MI, USA
ISSN 2191-8198 ISSN 2191-8201 (electronic) SpringerBriefs in Mathematics ISBN 978-3-319-92491-5 ISBN 978-3-319-92492-2 (eBook) https://doi.org/10.1007/978-3-319-92492-2 Library of Congress Control Number: 2018946786 Mathematics Subject Classification: 26B25, 49N15, 52A41, 60J60, 90C25, 91B16, 91B25, 91B26, 91B30, 91G10, 91G20 © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To Carol and Olivia To Lilly and Charles. And in memory of Jonathan Borwein (1951–2016) with respect.
Preface
Convex duality plays an essential role in many important financial problems. For example, it arises both in the minimization of conv
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