Mathematical Finance
Taking continuous-time stochastic processes allowing for jumps as its starting and focal point, this book provides an accessible introduction to the stochastic calculus and control of semimartingales and explains the basic concepts of Mathematical Finance
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Ernst Eberlein Jan Kallsen
Mathematical Finance
Springer Finance
Editorial Board Marco Avellaneda Giovanni Barone-Adesi Francesca Biagini Bruno Bouchard Mark Broadie Emanuel Derman Paolo Guasoni Mathieu Rosenbaum
Springer Finance Springer Finance is a programme of books addressing students, academics and practitioners working on increasingly technical approaches to the analysis of financial markets. It aims to cover a variety of topics, not only mathematical and computational finance but foreign exchange, term structure, risk management, portfolio theory, equity derivatives, energy finance and commodities, financial economics.
More information about this series at http://www.springer.com/series/3674
Ernst Eberlein • Jan Kallsen
Mathematical Finance
123
Ernst Eberlein Department of Mathematical Stochastics University of Freiburg Freiburg im Breisgau Germany
Jan Kallsen Department of Mathematics Kiel University Kiel Germany
ISSN 1616-0533 ISSN 2195-0687 (electronic) Springer Finance ISBN 978-3-030-26105-4 ISBN 978-3-030-26106-1 (eBook) https://doi.org/10.1007/978-3-030-26106-1 Mathematics Subject Classification (2010): 91G20, 91G80, 60G51, 60G44, 60H05, 60J75, 60H10, 91G10, 91G30, 93E20 JEL Classification: G13, G11, D52, C61 © Springer Nature Switzerland AG 2019 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, expressed 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 in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To Carl-Philipp, Friederike, Sophie and to Birgit, Dörte, Matthies
Preface
Mathematical finance provides a quantitative description of financial markets, more specifically markets for exchange-traded assets, using mostly dynamic stochastic models. It is used to tackle three basic issues. • Valuation of assets What can reasonably be said about the price of a financial
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