**Graduate Studies in Mathematics**

Volume: 70;
2013;
305 pp;
Hardcover

MSC: Primary 60; 91;
**Print ISBN: 978-0-8218-9490-3
Product Code: GSM/70.R**

List Price: $65.00

AMS Member Price: $52.00

MAA Member Price: $58.50

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#### Supplemental Materials

# Probability Theory in Finance: A Mathematical Guide to the Black-Scholes Formula, Second Edition

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*Seán Dineen*

The use of the Black-Scholes model and formula is pervasive in
financial markets. There are very few undergraduate textbooks
available on the subject and, until now, almost none written by
mathematicians. Based on a course given by the author, the goal of
this book is to introduce advanced undergraduates and beginning
graduate students studying the mathematics of finance to the
Black-Scholes formula. The author uses a first-principles approach,
developing only the minimum background necessary to justify
mathematical concepts and placing mathematical developments in
context.

The book skillfully draws the reader toward the art of thinking
mathematically and then proceeds to lay the foundations in analysis
and probability theory underlying modern financial mathematics. It
rigorously reveals the mathematical secrets of topics such 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 universe 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.

The second edition contains numerous revisions and additional
material designed to enhance the book's usability as a classroom text.
These changes include insights gleaned by the author after teaching
from the text, as well as comments and suggestions made by others who
used the book. Whereas the revised edition maintains the original
approach, format, and list of topics, most chapters are modified to
some extent; in addition, the rearrangement of material resulted in a
new chapter (Chapter 9).

With the modest prerequisite of a first course in calculus, the
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 interested in probability and financial mathematics.

#### Reviews & Endorsements

Dineen is doing something valuable by trying to find ways to communicate mathematics in a serious way to an audience that often gets little more than recipes and rules. It's a project definitely worth supporting.

-- MAA Reviews

In addition to the usual improvements in response to comments and suggestions, the new edition reflects the experience of teaching real analysis. ... Dineen is doing something valuable by trying to find ways to communicate mathematics in a serious way to an audience that often gets little more than recipes and rules. It's a project definitely worth supporting.

-- Fernando Q. Gouvêa, MAA Reviews

This book provides a thorough presentation of the mathematics behind the derivatives pricing formula. It is written for mathematicians as well as finance students or professionals ... very lucid ... an excellent choice for graduate students in mathematical finance as well as practitioners with the required background.

-- Ita Cirovic Donev, MAA Reviews

A neatly and lively written text that may be warmly recommended to undergraduates and graduate students in mathematics and finance.

-- EMS Newsletter

The author has done a very good job presenting the abstract probability theory needed to understand the derivation of the Black-Scholes formula, as well as the intuitive ideas, often simple, behind it. By starting with simple models in which the financial principles used can be clearly seen and then building smoothly toward the more complex model used in the Black-Scholes formula, the author allows the reader to appreciate the financial principles used even in the more complex settings. Furthermore, the exercises included after each chapter help the reader understand the material presented. ... Finally, the many historical footnotes often add insight and help bring the mathematics to life.

-- Errol Caby, AT&T Laboratories

For budding financial engineers, this is an outstanding introduction to the mathematics that underlies derivatives pricing theory. ... It also offers plenty of exercises that will help you build mastery.

Dineen won an award (Best Books of 2006) for providing a treatment of finanical engineering math that is simultaneously accessible and rigorous.

-- Glyn Holton, founder Contingency Analysis and Riskbook.com

... an excellent choice ... This book provides a thorough presentation of the mathematics behind the derivatives pricing formula. It is written for mathematicians as well as finance students or professionals.

-- MAA Reviews

... one of the author's aims is to entice the students by the beauty of mathematics, which he illustrates very well. If a course instructor teaching from the book succeeds in this, my guess is that the course will be a great success.

It outshines most of its competitors ... variety of nice exercises and solutions ...

-- Mathematical Reviews

# Table of Contents

## Probability Theory in Finance: A Mathematical Guide to the Black-Scholes Formula, Second Edition

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface ix10 free
- Money and markets 116 free
- Fair games 1732
- Set theory 2944
- Measurable functions 5974
- Probability spaces 7792
- Expected values 107122
- Continuity and integrability 143158
- Conditional expectation 165180
- Lebesgue measure 189204
- Martingales 209224
- The Black-Scholes formula 227242
- Stochastic integration 243258
- Solutions 281296
- Bibliography 299314
- Index 301316 free
- Back Cover Back Cover1322