Introduction to Stochastic Calculus

This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but

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Rajeeva L. Karandikar B. V. Rao

Introduction to Stochastic Calculus

Indian Statistical Institute Series Editors-in-chief B. V. Rajarama Bhat, Indian Statistical Institute, Bengaluru, Karnataka, India Abhay G. Bhatt, Indian Statistical Institute, New Delhi, India Joydeb Chattopadhyay, Indian Statistical Institute, Kolkata, West Bengal, India S. Ponnusamy, Indian Statistical Institute, Chennai, Tamil Nadu, India

The Indian Statistical Institute Series publishes high-quality content in the domain of mathematical sciences, bio-mathematics, financial mathematics, pure and applied mathematics, operations research, applied statistics and computer science and applications with primary focus on mathematics and statistics. Editorial board comprises of active researchers from major centres of Indian Statistical Institutes. Launched at the 125th birth Anniversary of P.C. Mahalanobis, the series will publish textbooks, monographs, lecture notes and contributed volumes. Literature in this series will appeal to a wide audience of students, researchers, educators, and professionals across mathematics, statistics and computer science disciplines.

More information about this series at http://www.springer.com/series/15910

Rajeeva L. Karandikar B. V. Rao •

Introduction to Stochastic Calculus

123

Rajeeva L. Karandikar Chennai Mathematical Institute Siruseri, Tamil Nadu India

B. V. Rao Chennai Mathematical Institute Siruseri, Tamil Nadu India

ISSN 2523-3114 ISSN 2523-3122 (electronic) Indian Statistical Institute Series ISBN 978-981-10-8317-4 ISBN 978-981-10-8318-1 (eBook) https://doi.org/10.1007/978-981-10-8318-1 The print edition is not for sale in India. Customers from India please order the print book from: Hindustan Book Agency, P-19 Green Park Extension, New Delhi 110016, India. Library of Congress Control Number: 2018931455 © Springer Nature Singapore Pte Ltd. 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 i