Telegraph Processes and Option Pricing
The telegraph process is a useful mathematical model for describing the stochastic motion of a particle that moves with finite speed on the real line and alternates between two possible directions of motion at random time instants. That is why it can be c
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Alexander D. Kolesnik Nikita Ratanov
Telegraph Processes and Option Pricing
SpringerBriefs in Statistics
For further volumes: http://www.springer.com/series/8921
Alexander D. Kolesnik Nikita Ratanov •
Telegraph Processes and Option Pricing
123
Alexander D. Kolesnik Institute of Mathematics and Computer Science Academy of Sciences of Moldova Numerical Analysis and Probability Kishinev Moldova
ISSN 2191-544X ISBN 978-3-642-40525-9 DOI 10.1007/978-3-642-40526-6
Nikita Ratanov Faculty of Economics Universidad del Rosario Bogotá Colombia
ISSN 2191-5458 (electronic) ISBN 978-3-642-40526-6 (eBook)
Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013947371 Ó The Author(s) 2013 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This book gives an introduction to the contemporary mathematical theory of noninteracting particles moving at finite velocity in one dimension with alternating directions, so-called the telegraph (or telegrapher’s) stochastic processes. The main objective is to give the basic properties of the one-dimensional telegraph processes and to present their applications to option pricing. The book contains both the well-known results and the most recent achievements in this field. The model of a mass-les
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