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 texts 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.

Autorentext

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.

Klappentext

An elementary introduction to probability and mathematical finance including a chapter on the Capital Asset Pricing Model (CAPM), a topic that is very popular among practitioners and economists.

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.

Inhalt

Preface.- Introduction.- Probability I: Introduction to Discrete Probability.- Portfolio Management and the Capital Asset Pricing Model.- Background on Options.- An Aperitif on Arbitrage.- Probability II: More Discrete Probability.- Discrete-Time Pricing Models.- The Cox-Ross-Rubinstein Model.- Probability III: Continuous Probability.- The Black-Scholes Option Pricing Formula.- Optimal Stopping and American Options.- Appendix: Convexity and Separation.