Editors:
- Offers new or improved methods for dealing with volatility of the financial market
- Includes concise discussion of modelling, analysis and numerical solution methods for nonlinear Black-Scholes equations
- Several sections devoted to GPU programming techniques for solving financial problems
- Special chapter on software includes the Computational Finance Toolbox that provides insights to the detailed implementation of the proposed methods
Part of the book series: Mathematics in Industry (MATHINDUSTRY, volume 25)
Part of the book sub series: The European Consortium for Mathematics in Industry (TECMI)
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Table of contents (30 chapters)
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Front Matter
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Modelling
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Front Matter
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Transformation Methods and Special Discretizations
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Front Matter
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About this book
This book discusses the state-of-the-art and open problems in computational finance. It presents a collection of research outcomes and reviews of the work from the STRIKE project, an FP7 Marie Curie Initial Training Network (ITN) project in which academic partners trained early-stage researchers in close cooperation with a broader range of associated partners, including from the private sector.
The aim of the project was to arrive at a deeper understanding of complex (mostly nonlinear) financial models and to develop effective and robust numerical schemes for solving linear and nonlinear problems arising from the mathematical theory of pricing financial derivatives and related financial products. This was accomplished by means of financial modelling, mathematical analysis and numerical simulations, optimal control techniques and validation of models.
In recent years the computational complexity of mathematical models employed in financial mathematics has witnessed tremendous growth. Advanced numerical techniques are now essential to the majority of present-day applications in the financial industry.
Special attention is devoted to a uniform methodology for both testing the latest achievements and simultaneously educating young PhD students. Most of the mathematical codes are linked into a novel computational finance toolbox, which is provided in MATLAB and PYTHON with an open access license. The book offers a valuable guide for researchers in computational finance and related areas, e.g. energy markets, with an interest in industrial mathematics.
Keywords
- nonlinear Black-Scholes equations
- Lie Algebra techniques
- Lévy methods
- high-dimensional partial differential equations
- optimal control techniques
- calibration
- positivity preservation
- artificial boundary condition
- transformation techniques
- mixed derivatives
- correlation
- model order reduction
- uncertainty quantification
- ADI-methods
- GPU programming
- partial differential equations
- quantitative finance
Editors and Affiliations
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Lehrstuhl für Angewandte Mathematik/Numerische Analysis, Bergische Universität Wuppertal, Wuppertal, Germany
Matthias Ehrhardt, Michael Günther, E. Jan W. ter Maten
About the editors
Bibliographic Information
Book Title: Novel Methods in Computational Finance
Editors: Matthias Ehrhardt, Michael Günther, E. Jan W. ter Maten
Series Title: Mathematics in Industry
DOI: https://doi.org/10.1007/978-3-319-61282-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-61281-2Published: 28 September 2017
Softcover ISBN: 978-3-319-87040-3Published: 17 May 2018
eBook ISBN: 978-3-319-61282-9Published: 19 September 2017
Series ISSN: 1612-3956
Series E-ISSN: 2198-3283
Edition Number: 1
Number of Pages: XVIII, 606
Number of Illustrations: 101 b/w illustrations, 93 illustrations in colour
Topics: Partial Differential Equations, Game Theory, Economics, Social and Behav. Sciences, Quantitative Finance, Computational Mathematics and Numerical Analysis, Probability Theory and Stochastic Processes