Steven Roman – Introduction to the Mathematics of Finance: From Risk Management to Options Pricing

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Introduction to the Mathematics of Finance
From Risk Management to Options Pricing

Authors: Steven Roman
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

Table of contents (11 chapters)

Front Matter
Pages i-xv

Introduction
Steven Roman
Pages 1-6

Probability I: An Introduction to Discrete Probability
Steven Roman
Pages 7-39

Portfolio Management and the Capital Asset Pricing Model
Steven Roman
Pages 41-77

Background on Options
Steven Roman
Pages 79-87

An Aperitif on Arbitrage
Steven Roman
Pages 89-101

Probability II: More Discrete Probability
Steven Roman
Pages 103-138

Discrete-Time Pricing Models
Steven Roman
Pages 139-185

The Cox-Ross-Rubinstein Model
Steven Roman
Pages 187-201

Probability III: Continuous Probability
Steven Roman
Pages 203-235

The Black-Scholes Option Pricing Formula
Steven Roman
Pages 237-275

Optimal Stopping and American Options
Steven Roman
Pages 277-303

Back Matter
Pages 305-356

About this book
The Mathematics of Finance has become a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced 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. The final chapter is devoted to American options.

The mathematics is not watered down, but is appropriate for the intended audience. No measure theory is used, and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a “need-to-know” basis. No background in finance is required, since the book also contains a chapter on options.

Reviews
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)

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.

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