The book aims to provide the reader with a mathematical foundation for an in-depth study of financial mathematics. The author has chosen to explain the techniques necessary to understand the Black-Scholes formula, currently one of the most successful and best-known applications of mathematics to finance, as his ultimate goal, thus providing an excellent focus for the reader's motivation.

Gradually and sympathetically, the book draws the reader towards the art of thinking mathematically and then proceeds to lay the foundations in analysis and probability theory underlying modern financial mathematics. It manages to reveal rigorously the mathematical secrets of such topics as abstract measure theory, conditional expectations, martingales, Wiener processes, the Itô calculus, and other ingredients of the Black-Scholes formula. In explaining these topics, the author uses examples drawn from the world of finance. The book also contains many exercises, some included to clarify simple points of exposition, others to introduce new ideas and techniques, and a few containing relatively deep mathematical results.

With the modest prerequisite of a first course in calculus, this book is suitable for undergraduates and graduate students in mathematics, finance, and economics and can be read, using appropriate selections, at a number of levels.

Readership

Undergraduate and graduate students in mathematics, economics, or finance interested in studying probability theory and other mathematics used in finance.