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© 2004

Introduction to the Mathematics of Finance

From Risk Management to Options Pricing

Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Steven Roman
    Pages 1-6
  3. Steven Roman
    Pages 79-87
  4. Steven Roman
    Pages 89-101
  5. Steven Roman
    Pages 103-138
  6. Steven Roman
    Pages 139-185
  7. Steven Roman
    Pages 187-201
  8. Steven Roman
    Pages 203-235
  9. Steven Roman
    Pages 237-275
  10. Steven Roman
    Pages 277-303
  11. Back Matter
    Pages 305-356

About this book

Introduction

The Mathematics of Finance has become a hot topic in applied mathematics ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for upper division undergraduate or beginning graduate students in mathematics, finance or economics. With the exception of an optional chapter on the Capital Asset Pricing Model, the book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model. The final chapter is devoted to American options.

The mathematics is not watered down but is appropriate for the intended audience. No measure theory is used and only a small amount of linear algebra is required. All necessary probability theory is developed in several chapters throughout the book, on a "need-to-know" basis. No background in finance is required, since the book also contains a chapter on options.

The author is Emeritus Professor of Mathematics, having taught at a number of universities, including MIT, UC Santa Barabara, the University of South Florida and the California State University, Fullerton. He has written 27 books in mathematics at various levels and 9 books on computing. His interests lie mostly in the areas of algebra, set theory and logic, probability and finance. When not writing or teaching, he likes to make period furniture, copy Van Gogh paintings and listen to classical music. He also likes tofu.

Keywords

arbitrage asset pricing Black-Scholes information theory linear algebra mathematical finance mathematics measure measure theory probability probability theory risk management

Authors and affiliations

  1. 1.California State University FullertonFullertonUSA

About the authors

Dr. Roman has authored 32 books, including a number of books on mathematics, such as Coding and Information Theory, Advanced Linear Algebra, and Field Theory, published by Springer-Verlag. He has also written Modules in Mathematics, a series of 15 small books designed for the general college-level liberal arts student. Besides his books for O'Reilly, Dr. Roman has written two other computer books, both published by Springer-Verlag.

Bibliographic information

  • Book Title Introduction to the Mathematics of Finance
  • Book Subtitle From Risk Management to Options Pricing
  • Authors Steven Roman
  • Series Title Undergraduate Texts in Mathematics
  • DOI https://doi.org/10.1007/978-1-4419-9005-1
  • Copyright Information Steven Roman 2004
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-21375-0
  • Softcover ISBN 978-0-387-21364-4
  • eBook ISBN 978-1-4419-9005-1
  • Series ISSN 0172-6056
  • Edition Number 1
  • Number of Pages XV, 356
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Quantitative Finance
    Probability Theory and Stochastic Processes
    Finance, general
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking

Reviews

From the reviews of the first edition:

"The book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formula as a limiting case of the Cox-Ross-Rubinstein discrete model. … The mathematics is not watered down but is appropriate for the intended audience. … No background in finance is required, since the book also contains a chapter on options." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 50 (3-4), 2004)

"The book is basically a textbook on the mathematics of financial derivatives on equity … . The text covers the material with precision, with detailed discussions, not avoiding the topics that require a bit more of mathematical maturity, and this it does with clarity. In particular, the discussion of optimal stopping is clear and detailed." (Eusebio Corbache, Zentralblatt MATH, Vol. 1068, 2005)