**AMS/MAA Textbooks**

Volume: 49;
2019;
232 pp;
Hardcover

MSC: Primary 91; 97;
Secondary 60; 65; 35

**Print ISBN: 978-1-4704-4839-4
Product Code: TEXT/49**

List Price: $75.00

AMS Member Price: $56.25

MAA Member Price: $56.25

**Electronic ISBN: 978-1-4704-5204-9
Product Code: TEXT/49.E**

List Price: $75.00

AMS Member Price: $56.25

MAA Member Price: $56.25

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#### Supplemental Materials

# Mathematical Modeling in Economics and Finance: Probability, Stochastic Processes, and Differential Equations

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*Steven R. Dunbar*

MAA Press: An Imprint of the American Mathematical Society

Mathematical Modeling in Economics and Finance
is designed as a textbook for an upper-division course on modeling in
the economic sciences. The emphasis throughout is on the modeling
process including post-modeling analysis and criticism. It is a
textbook on modeling that happens to focus on financial instruments
for the management of economic risk. The book combines a study of
mathematical modeling with exposure to the tools of probability
theory, difference and differential equations, numerical simulation,
data analysis, and mathematical analysis.

Students taking a course from Mathematical Modeling in Economics
and Finance will come to understand some basic stochastic processes
and the solutions to stochastic differential equations. They will
understand how to use those tools to model the management of financial
risk. They will gain a deep appreciation for the modeling process and
learn methods of testing and evaluation driven by data. The reader of
this book will be successfully positioned for an entry-level position
in the financial services industry or for beginning graduate study in
finance, economics, or actuarial science.

The exposition in Mathematical Modeling in Economics and Finance is
crystal clear and very student-friendly. The many exercises are
extremely well designed. Steven Dunbar is Professor Emeritus of
Mathematics at the University of Nebraska and he has won both
university-wide and MAA prizes for extraordinary teaching. Dunbar
served as Director of the MAA's American Mathematics Competitions from
2004 until 2015. His ability to communicate mathematics is on full
display in this approachable, innovative text.

#### Readership

Undergraduate and graduate students interested in mathematical finance.

#### Reviews & Endorsements

I think a student working through this text would have a remarkable conclusion to an undergraduate mathematical career that would prepare them for graduate work. I look forward to the opportunity to teach out of this textbook.

-- Andrew O. Hall, Marymount University

The uniqueness of this book is rooted in merging several different areas of mathematics and robust quantitative reasoning...By integrating various areas the author created a book that is not only easy to read and learn from but also enjoyable. Its wide audience that includes undergraduate students in mathematics, economics, finance, actuarial science but also in physical science, computer science and engineering proves that the author selected the delivery methods in a sense that are applicable to many academic disciplines.

-- Andrzej Sokolowski, MAA Reviews

#### Table of Contents

# Table of Contents

## Mathematical Modeling in Economics and Finance: Probability, Stochastic Processes, and Differential Equations

- Cover Cover11
- Title page iii4
- Copyright iv5
- Contents vii8
- Preface ix10
- Chapter 1. Background 118
- Chapter 2. Binomial Models 5168
- Chapter 3. First Step Analysis 6582
- Chapter 4. Limit Theorems for Coin Tossing 95112
- Chapter 5. Brownian Motion 113130
- 5.1. Intuitive Introduction to Diffusions 113130
- 5.2. The Definition of Brownian Motion* and the Wiener Process 118135
- 5.3. Approximation of Brownian Motion* by Coin Tossing Sums 125142
- 5.4. Transformations of the Wiener Process 129146
- 5.5. Hitting Times and Ruin Probabilities 133150
- 5.6. Path Properties of Brownian Motion 137154
- 5.7. Quadratic Variation of the Wiener Process 141158

- Chapter 6. Stochastic Calculus 149166
- Chapter 7. The Black–Scholes Equation 179196
- Endnotes 221238
- Bibliography 225242
- Index 229246
- Back Cover Back Cover1250