Overview
Provides a concise and up-to-date introduction for all graduate students studying finance/quantitative finance
Includes a wealth of examples and exercises to promote student comprehension
Discusses the Black-Scholes equation to help students understand the mathematical underpinning of financial instruments
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Table of contents (16 chapters)
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Front Matter
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Introduction
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Front Matter
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Linear Algebra
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Front Matter
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Calculus
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Front Matter
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Quantum Mathematics
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Front Matter
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Keywords
- Square matrices
- Indefinite integrals
- Hessian matrix
- Gaussian integration
- Quantitative finance
- Separable diffferential equations
- Discrete random variables
- Probability distribution functions
- Lognormal stock price
- Black-Scholes-Schrodinger equation
- Risk-Neutral Martingale solution
- Linear Langevin equation
- Hedged portfolio
About this book
The content is divided into five major sections: mathematical methods are covered in the first four sections, and can be taught in one semester. The book begins by focusing on the core subjects of linear algebra and calculus, before moving on to the more advanced topics of probability theory and stochastic calculus. Detailed derivations of the Black-Scholes and Merton equations are provided – in order to clarify the mathematical underpinnings of stochastic calculus. Each chapter of the first four sections includes a problem set, chiefly drawn from economics and finance.
In turn, section five addresses quantum mathematics. The mathematical topics covered in the first four sections are sufficient for the study of quantum mathematics; Black-Scholes option theory and Merton’s theory of corporate debt are among topics analyzed using quantum mathematics.
Authors and Affiliations
About the author
Prof. Belal Ehsan Baaquie holds a B.S. in Physics from Caltech and a Ph.D. in Theoretical Physics from Cornell University, USA. His main research interest is in the study and application of mathematical methods from quantum field theory. He has applied the mathematical formalism of field theory to finance and been a major contributor to the emerging field of quantum finance. His current focus is on developing the formalism of quantum finance and applying it to option pricing, corporate coupon bonds, and the theory of interest rates, as well as the study of equity, foreign exchange, and commodities. He is also applying methodologies from statistical mechanics and quantum field theory to the study of microeconomics and macroeconomics.
Bibliographic Information
Book Title: Mathematical Methods and Quantum Mathematics for Economics and Finance
Authors: Belal Ehsan Baaquie
DOI: https://doi.org/10.1007/978-981-15-6611-0
Publisher: Springer Singapore
eBook Packages: Economics and Finance, Economics and Finance (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020
Hardcover ISBN: 978-981-15-6610-3Published: 11 August 2020
Softcover ISBN: 978-981-15-6613-4Published: 12 August 2021
eBook ISBN: 978-981-15-6611-0Published: 10 August 2020
Edition Number: 1
Number of Pages: XXIII, 432
Number of Illustrations: 47 b/w illustrations, 31 illustrations in colour
Topics: Economic Theory/Quantitative Economics/Mathematical Methods, Quantitative Finance, Statistics for Business, Management, Economics, Finance, Insurance