Numerical Solution of Stochastic Differential Equations with Jumps in Finance
In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of
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Stochastic Modelling and Applied Probability (Formerly: Applications of Mathematics)
64
Edited by B. Rozovski˘ı G. Grimmett Advisory Board M. Hairer I. Karatzas F.P. Kelly A. Kyprianou Y. Le Jan B. Øksendal G. Papanicolaou E. Pardoux E. Perkins
For other titles in this series, go to http://www.springer.com/series/602
Eckhard Platen
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Nicola Bruti-Liberati
Numerical Solution of Stochastic Differential Equations with Jumps in Finance
Eckhard Platen Nicola Bruti-Liberati (1975–2007) School of Finance and Economics Department of Mathematical Sciences University of Technology, Sydney PO Box 123 Broadway NSW 2007 Australia [email protected]
Managing Editors Boris Rozovski˘ı Division of Applied Mathematics Brown University 182 George St Providence, RI 02912 USA [email protected]
Geoffrey Grimmett Centre for Mathematical Sciences University of Cambridge Wilberforce Road Cambridge CB3 0WB UK [email protected]
ISSN 0172-4568 ISBN 978-3-642-12057-2 e-ISBN 978-3-642-13694-8 DOI 10.1007/978-3-642-13694-8 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010931518 Mathematics Subject Classification (2010): 60H10, 65C05, 62P05 © Springer-Verlag Berlin Heidelberg 2010 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 permission for use must always be obtained from Springer. Violations are liable to 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: deblik Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This research monograph concerns the design and analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by Wiener processes and Poisson processes or Poisson jump measures. In financial and actuarial modeling and other areas of application, such jump diffusions are often used to describe the dynamics of various state variables. In finance these may represent, for instance, asset prices, credit ratings, stock indices, interest rates, exchange rates or commodity prices. The jump component can capture event-driven uncertainties, such as corporate defaults, operational failures or insured events. The book focuses on efficient and numerically stable strong and weak discrete-time approximations of solutions of SDEs. Strong approximations provide efficient tools for simulation problems such as those arising in
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