Numerical Methods in Finance Bordeaux, June 2010
Numerical methods in finance have emerged as a vital field at the crossroads of probability theory, finance and numerical analysis. Based on presentations given at the workshop Numerical Methods in Finance held at the INRIA Bordeaux (France) on June 1-2,
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Ren´e A. Carmona Pierre Del Moral Peng Hu Nadia Oudjane Editors
Numerical Methods in Finance Bordeaux, June 2010
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Editors Ren´e A. Carmona Bendheim Center for Finance Department of Operations Research and Financial Engineering Princeton University Princeton, NJ USA Pierre Del Moral Centre INRIA Bordeaux Sud-Ouest and Institut de Math´ematiques de Bordeaux Universit´e Bordeaux I Talence France
Peng Hu Centre INRIA Bordeaux Sud-Ouest and Institut de Math´ematiques de Bordeaux Universit´e Bordeaux I Talence France Nadia Oudjane EDF R&D and Fime Laboratoire de Finance des March´es de l’Energie Clamart France
and Centre de Math´ematiques Appliqu´ees ´ Ecole Polytechnique CNRS Palaiseau France
ISSN 2190-5614 e-ISSN 2190-5622 ISBN 978-3-642-25745-2 e-ISBN 978-3-642-25746-9 DOI 10.1007/978-3-642-25746-9 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2012934046 Mathematical Subject Classification (2010): 91B28, 60G40, 93E20, 91G60 c Springer-Verlag Berlin Heidelberg 2012 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. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The history of mathematical and numerical finance starts in 1900, with the seminal thesis of Louis Bachelier, Th´eorie de la Sp´eculation, which introduced Brownian motion in order to model stock price movements and evaluate options. Not only did this remarkable work modeled the randomness of stock prices in a mathematical framework germane to the popular Nobel Prize in Economics winning solution propos
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