An Introduction to Mathematical Finance with Applications Understand
This textbook aims to fill the gap between those that offer a theoretical treatment without many applications and those that present and apply formulas without appropriately deriving them. The balance achieved will give readers a fundamenta
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Arlie O. Petters Xiaoying Dong
An Introduction to Mathematical Finance with Applications Understanding and Building Financial Intuition
Springer Undergraduate Texts in Mathematics and Technology Series Editors: J.M. Borwein H. Holden V.H. Moll
More information about this series at http://www.springer.com/series/7438
Arlie O. Petters • Xiaoying Dong
An Introduction to Mathematical Finance with Applications Understanding and Building Financial Intuition
123
Arlie O. Petters Department of Mathematics Duke University Durham, NC, USA
Xiaoying Dong Department of Mathematics Duke University Durham, NC, USA
ISSN 1867-5506 ISSN 1867-5514 (electronic) Springer Undergraduate Texts in Mathematics and Technology ISBN 978-1-4939-3781-3 ISBN 978-1-4939-3783-7 (eBook) DOI 10.1007/978-1-4939-3783-7 Library of Congress Control Number: 2016939449 Mathematics Subject Classification (2010): 91Gxx © Arlie O. Petters and Xiaoying Dong 2016 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. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
To my loving wife, Elizabeth Petters, for being at my side unconditionally and my child, Preston Petters, who inspires me with his intense curiosity. A.O. Petters
To my dear husband and best friend, Xin Zhou. I could not imagine to complete my part of the contribution to this book without his love and support. X. Dong
Preface
Rationale and Aim Given the increasing intricacies and interconnectedness of financial firms’ activities and the potential opportunities and risks to which they expose themselves and the world’s economy, the next generation of financial engineers needs to master an extensive array of mathematical financial models. Indeed, one of the current challenges in finance is that the complexity of modern securities and markets has forced modelers to employ increasingly sophisticated mathematical tools to address financial issues, cr
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