Advanced Mathematical Methods for Finance
This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information i
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Giulia Di Nunno Bernt Øksendal Editors
Advanced Mathematical Methods for Finance
Editors Giulia Di Nunno Bernt Øksendal CMA, Department of Mathematics University of Oslo P.O. Box 1053, Blindern 0316 Oslo, Norway and Norwegian School of Economics and Business Administration Helleveien 30 5045 Bergen, Norway [email protected] [email protected]
ISBN 978-3-642-18411-6 e-ISBN 978-3-642-18412-3 DOI 10.1007/978-3-642-18412-3 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011925381 Mathematics Subject Classification (2010): 91Gxx, 91G10, 91G20, 91G40, 91G70, 91G80, 91B16, 91B30, 91B70, 93E11, 93E20, 60E15, 60G15, 60G22, 60G40, 60G44, 60G51, 60G57, 60G60, 60H05, 60H07, 60H10, 60H15, 60H20, 60H30, 60H40, 60J65, 60K15, 62G07, 62G08, 62M07, 62P20, 41A25, 46B70, 94Axx, 35F20, 35Q35 © Springer-Verlag Berlin Heidelberg 2011 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
The title of this volume “Advanced Mathematical Methods for Finance,” AMaMeF for short, originates from the European network of the European Science Foundation with the same name that started its activity in 2005. The goals of its program have been the development and the use of advanced mathematical tools for finance, from theory to practice. This book was born in the same spirit of the program. It presents innovations in the mathematical methods in various research areas representing the broad spectrum of AMaMeF itself. It covers the mathematical foundations of financial analysis, numerical methods, and the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced at various levels. The chosen blending of topics gives a large view of the up-to-date frontiers of the mathematics for finance. This volume represents the joint work of European exper
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