Financial Mathematics

J Robert Buchanan

Like many university professors, I enjoy teaching and search for the right book for each course I teach. In 2001 when I developed a course in financial mathematics for undergraduate mathematics majors, I felt that no existing book combined the right mathematical, statistical, economic, and financial elements for students at Millersville University. After teaching the course, cobbling together lecture notes from a number of different sources, all of which presented some but not all things well, I decided to write my own textbook. The ultimate goal was to have it published so that it would be available to students and professors everywhere. I was very fortunate to find a publisher (World Scientific Publishing) willing to take a chance on a first-time author. The book in question An Undergraduate Introduction to Financial Mathematics, J. Robert Buchanan, World Scientific Publishing Company, Hackensack, NJ, USA, appeared in 2006. The second and third editions appeared in 2008 and 2012 respectively. The first and second editions are now out of stock. At the risk of sounding like a advertisement for WSPC, I want to say that all the people I dealt with there were exceptionally professional and it was a pleasure to work them.

I am thankful to all the readers of the first, second, and third editions who took the time to send me comments and pointers to errors and typos in the third edition. If you would like to purchase a copy of this book please check the publisher's website. The text is also available from online book retailers such as and in e-book format from iTunes.

I am pleased with the messages of encouragement and other comments that readers and reviewers of the book have sent to me. I hope that people looking for a gentle introduction to the mathematics of financial engineering will find the book useful. In return readers can help improve the third edition by sending me any suggestions, corrections, or other ideas for improvement. If I am able to use your suggestion I will certainly mention you by name and affiliation in the preface of the book. Corrections to the text are especially valuable. If you believe you have spotted an error, please send me a description of the error (including its location in the book) and I will update the list of errata for the third edition.

Instructors teaching from my textbook may wish to use a set of PDF files I have created for each chapter for use in the classroom. Please contact me with any corrections of comments on them. A zip file archive of the entire collection is also available. Links to individual chapters are below.

  1. The Theory of Interest
  2. Discrete Probability
  3. Normal Random Variables and Probability
  4. The Arbitrage Theorem
  5. Random Walks and Brownian Motion
  6. Forwards and Futures
  7. Options
  8. Solution of the Black-Scholes Equation
  9. Derivatives of the Black-Scholes Option Prices
  10. Extensions to the Black-Scholes Equation
  11. Hedging
  12. Optimizing Portfolios
  13. American Options
Undergraduate Introduction to
Financial Mathematics, 1st edition Undergraduate Introduction to
Financial Mathematics, 2nd edition

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