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Introduction to the Mathematics of Finance


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Table of Contents

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.

About the Author

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.


From the reviews of the first edition:

"The book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formula as a limiting case of the Cox-Ross-Rubinstein discrete model. ... The mathematics is not watered down but is appropriate for the intended audience. ... No background in finance is required, since the book also contains a chapter on options." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 50 (3-4), 2004)

"The book is basically a textbook on the mathematics of financial derivatives on equity ... . The text covers the material with precision, with detailed discussions, not avoiding the topics that require a bit more of mathematical maturity, and this it does with clarity. In particular, the discussion of optimal stopping is clear and detailed." (Eusebio Corbache, Zentralblatt MATH, Vol. 1068, 2005)

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