Mathematics for Finance: An Introduction to Financial Engineering (Springer Undergraduate Mathematics Series)

This textbook contains the fundamentals for an undergraduate course in mathematical finance aimed primarily at students of mathematics. Assuming only a basic knowledge of probability and calculus, the material is presented in a mathematically rigorous and complete way. The book covers the time value of money, including the time structure of interest rates, bonds and stock valuation; derivative securities (futures, options), modelling in discrete time, pricing and hedging, and many other core topics. With numerous examples, problems and exercises, this book is ideally suited for independent study.

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 economic concepts ... . 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)