Mathematics for Finance

1. Front Matter

   Pages i-x

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2. Introduction: A Simple Market Model

   Pages 1-20

3. Risk-Free Assets

   Pages 21-45

4. Risky Assets

   Pages 47-71

5. Discrete Time Market Models

   Pages 73-90

6. Portfolio Management

   Pages 91-124

7. Forward and Futures Contracts

   Pages 125-145

8. Options: General Properties

   Pages 147-172

9. Option Pricing

   Pages 173-190

10. Financial Engineering

    Pages 191-214

11. Variable Interest Rates

    Pages 215-236

12. Stochastic Interest Rates

    Pages 237-261

13. Back Matter

    Pages 263-310

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Designed to form the basis of an undergraduate course in mathematical finance, this book builds on mathematical models of bond and stock prices and covers three major areas of mathematical finance that all have an enormous impact on the way modern financial markets operate, namely: Black-Scholes’ arbitrage pricing of options and other derivative securities; Markowitz portfolio optimization theory and the Capital Asset Pricing Model; and interest rates and their term structure. Assuming only a basic knowledge of probability and calculus, it covers the material in a mathematically rigorous and complete way at a level accessible to second or third year undergraduate students. The text is interspersed with a multitude of worked examples and exercises, so it is ideal for self-study and suitable not only for students of mathematics, but also students of business management, finance and economics, and anyone with an interest in finance who needs to understand the underlying theory.

• Arbitrage
• Derivative Securities
• Finance
• Financial Engineering
• Mathematical Finance
• Portfolio Theory
• Risk Management
• optimization
• quantitative finance

From the reviews:

"This text is an excellent introduction to Mathematical Finance. Armed with a knowledge of basic calculus and probability a student can use this book to learn about derivatives, interest rates and their term structure and portfolio management. The text serves as an easily understood introduction to the economic concepts but also manages to cover the topics in a mathematically rigorous manner."

Zentralblatt MATH

"For the most part, the authors employ just pre-calculus and basic probability theory. Almost all concepts are presented in discrete time. Only later in the book is a small account of calculus and linear algebra used. Given these basic tools, it is surprising how high a level of sophistication the authors achieve, covering such topics as arbitrage-free valuation, binomial trees, and risk-neutral valuation... Despite its elementary nature, the book is mathematically VERY formal. This is excellent for clarifying definitions. Notions such as arbitrage or admissible portfolio are indicated with mathematical precision. The result is mathematically elegant and will appeal to students who have a degree of mathematical sophistication."

www.riskbook.com

"As the authors modestly announce … the book ‘is an excellent financial investment. … The level of exposition is pretty basic … . That makes the book accessible to second year undergraduate students (not only for students of mathematics, but hopefully also for students of business management, finance and economics). … the overall impression of the book is quite positive. The reviewer can only congratulate the authors with successful completion of a difficult task of writing a useful textbook on a traditionally hard topic." (K. Borovkov, The Australian Mathematical Society Gazette, Vol. 31 (4), 2004)

"This text is an excellent introduction to Mathematical Finance. … The text serves as an easily understood introduction to the economicconcepts … . The book contains many worked examples and exercises and would make a useful textbook for a first course in Financial Mathematics." (Julann O’Shea, Zentralblatt MATH, Vol. 1035, 2004)

"Designed to form the basis of an undergraduate course in mathematical finance, the text builds on mathematical models of bond and stock prices … . It covers the material … at a level accessible to second or third year undergraduate students. … provides ample material for tutorials, and makes the book ideal for self-study. It is suitable not only for students of mathematics, but also students of business management, finance and economics, and anyone with an interest in finance … ." (Zentralblatt für Didaktik der Mathematik, August, 2004)

"The book … is designed as a textbook for an undergraduate course aimed at 2nd or 3rd year mathematics students and also of business management or economics. … the authors have tried to aim their book at too wide a potential readership. … the authors have written a very useful book. … are to be applauded for the broad scope of this book. … The book contains a number of exercises … . Worked solutions are given at the back … . " (David Applebaum, The Mathematical Gazette, Vol. 88 (512), 2004)

• Nowy Sącz School of Business-National Louis University, Nowy Sącz, Poland

  Marek Capiński

• Department of Mathematics, University of Hull, Kingston upon Hull, UK

  Tomasz Zastawniak

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