Overview
- Provides a gentle introduction to the calculus and control for stochastic processes with jumps
- Covers Lévy and affine processes as well as their applications in financial modelling
- Compares and explains the rationale behind different valuation and hedging concepts
Part of the book series: Springer Finance (FINANCE)
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Table of contents (14 chapters)
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Front Matter
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Stochastic Calculus
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Front Matter
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Back Matter
Keywords
About this book
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 such as arbitrage theory, hedging, valuation principles, portfolio choice, and term structure modelling. It bridges thegap between introductory texts and the advanced literature in the field.
Most textbooks on the subject are limited to diffusion-type models which cannot easily account for sudden price movements. Such abrupt changes, however, can often be observed in real markets. At the same time, purely discontinuous processes lead to a much wider variety of flexible and tractable models. This explains why processes with jumps have become an established tool in the statistics and mathematics of finance.
Graduate students, researchers as well as practitioners will benefit from this monograph.
Reviews
“This masterpiece on mathematical finance is written by two leading authorities in the field. It provides an excellent treatment of important topics in mathematical finance. … A nice feature of the monograph is that the intuitions and practical motivations of theories, methods and models are well explained. … Another nice feature of the monograph is that problems or exercises are provided in each of the chapters. A chapter-by-chapter review of the monograph is presented in the sequel.” (Tak Kuen Siu, zbMATH 1452.91001, 2021)
Authors and Affiliations
About the authors
Ernst Eberlein is professor emeritus at the University of Freiburg. After studying mathematics and physics at the universities of Erlangen and Paris, he received a Dr. rer. nat. at the University of Erlangen-Nürnberg and his habilitation in mathematics from ETH Zürich. For a period of ten years he served as Executive Secretary of the Bachelier Finance Society. From 2006 to 2013 he acted as co-editor of the journal Mathematical Finance.
Jan Kallsen is professor of mathematics at Kiel University. Having studied Mathematics and Physics in Kiel, Freiburg, Boston and Vienna, he received a Dr. rer. nat. and his habilitation from the University of Freiburg. Before coming to Kiel he held a position as professor of Mathematical Finance at the Technical University of Munich.
Bibliographic Information
Book Title: Mathematical Finance
Authors: Ernst Eberlein, Jan Kallsen
Series Title: Springer Finance
DOI: https://doi.org/10.1007/978-3-030-26106-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-26105-4Published: 12 December 2019
Softcover ISBN: 978-3-030-26108-5Published: 21 December 2020
eBook ISBN: 978-3-030-26106-1Published: 03 December 2019
Series ISSN: 1616-0533
Series E-ISSN: 2195-0687
Edition Number: 1
Number of Pages: XVII, 772
Number of Illustrations: 2 b/w illustrations, 32 illustrations in colour
Topics: Quantitative Finance, Probability Theory and Stochastic Processes, Financial Engineering, Risk Management, Financial Mathematics