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Mathematical Modeling in Economics and Finance: Probability, Stochastic Processes, and Differential Equations
 
Steven R. Dunbar :  University of Nebraska–Lincoln, Lincoln, NE
Mathematical Modelingin Economics and Finance
MAA Press: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-1-4704-4839-4
Product Code:  TEXT/49
List Price: $75.00
MAA Member Price: $56.25
AMS Member Price: $56.25
eBook ISBN:  978-1-4704-5204-9
Product Code:  TEXT/49.E
List Price: $69.00
MAA Member Price: $51.75
AMS Member Price: $51.75
Hardcover ISBN:  978-1-4704-4839-4
eBook: ISBN:  978-1-4704-5204-9
Product Code:  TEXT/49.B
List Price: $144.00 $109.50
MAA Member Price: $108.00 $82.13
AMS Member Price: $108.00 $82.13
Add to cart
Mathematical Modelingin Economics and Finance
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Mathematical Modeling in Economics and Finance: Probability, Stochastic Processes, and Differential Equations
Steven R. Dunbar :  University of Nebraska–Lincoln, Lincoln, NE
MAA Press: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-1-4704-4839-4
Product Code:  TEXT/49
List Price: $75.00
MAA Member Price: $56.25
AMS Member Price: $56.25
eBook ISBN:  978-1-4704-5204-9
Product Code:  TEXT/49.E
List Price: $69.00
MAA Member Price: $51.75
AMS Member Price: $51.75
Hardcover ISBN:  978-1-4704-4839-4
eBook ISBN:  978-1-4704-5204-9
Product Code:  TEXT/49.B
List Price: $144.00 $109.50
MAA Member Price: $108.00 $82.13
AMS Member Price: $108.00 $82.13
Add to cart
  • Book Details
     
     
    AMS/MAA Textbooks
    Volume: 49; 2019; 232 pp
    MSC: Primary 91; 97; Secondary 60; 65; 35

    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.
  • Table of Contents
     
     
    • Cover
    • Title page
    • Copyright
    • Contents
    • Preface
    • Chapter 1. Background
    • 1.1. Brief History of Mathematical Finance
    • 1.2. Options and Derivatives
    • 1.3. Speculation and Hedging
    • 1.4. Arbitrage
    • 1.5. Mathematical Modeling
    • 1.6. Randomness
    • 1.7. Stochastic Processes
    • 1.8. A Model of Collateralized Debt Obligations
    • Chapter 2. Binomial Models
    • 2.1. Single Period Binomial Models
    • 2.2. Multiperiod Binomial Tree Models
    • Chapter 3. First Step Analysis
    • 3.1. A Coin Tossing Experiment
    • 3.2. Ruin Probabilities
    • 3.3. Duration of the Gambler’s Ruin
    • 3.4. A Stochastic Process Model* of Cash Management
    • Chapter 4. Limit Theorems for Coin Tossing
    • 4.1. Laws of Large Numbers
    • 4.2. Moment Generating Functions
    • 4.3. The Central Limit Theorem
    • Chapter 5. Brownian Motion
    • 5.1. Intuitive Introduction to Diffusions
    • 5.2. The Definition of Brownian Motion* and the Wiener Process
    • 5.3. Approximation of Brownian Motion* by Coin Tossing Sums
    • 5.4. Transformations of the Wiener Process
    • 5.5. Hitting Times and Ruin Probabilities
    • 5.6. Path Properties of Brownian Motion
    • 5.7. Quadratic Variation of the Wiener Process
    • Chapter 6. Stochastic Calculus
    • 6.1. Stochastic Differential Equations
    • 6.2. Itô’s Formula
    • 6.3. Properties of Geometric Brownian Motion
    • 6.4. Models of Stock Market Prices
    • Chapter 7. The Black–Scholes Equation
    • 7.1. Derivation of the Black–Scholes Equation
    • 7.2. Solution of the Black–Scholes Equation
    • 7.3. Put-Call Parity
    • 7.4. Implied Volatility
    • 7.5. Sensitivity, Hedging, and the Greeks
    • 7.6. Limitations of the Black–Scholes Model
    • Endnotes
    • Bibliography
    • Index
    • Back Cover
  • Additional Material
     
     
  • Reviews
     
     

    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Accessibility – to request an alternate format of an AMS title
AMS/MAA Textbooks
Volume: 49; 2019; 232 pp
MSC: Primary 91; 97; Secondary 60; 65; 35

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.
  • Cover
  • Title page
  • Copyright
  • Contents
  • Preface
  • Chapter 1. Background
  • 1.1. Brief History of Mathematical Finance
  • 1.2. Options and Derivatives
  • 1.3. Speculation and Hedging
  • 1.4. Arbitrage
  • 1.5. Mathematical Modeling
  • 1.6. Randomness
  • 1.7. Stochastic Processes
  • 1.8. A Model of Collateralized Debt Obligations
  • Chapter 2. Binomial Models
  • 2.1. Single Period Binomial Models
  • 2.2. Multiperiod Binomial Tree Models
  • Chapter 3. First Step Analysis
  • 3.1. A Coin Tossing Experiment
  • 3.2. Ruin Probabilities
  • 3.3. Duration of the Gambler’s Ruin
  • 3.4. A Stochastic Process Model* of Cash Management
  • Chapter 4. Limit Theorems for Coin Tossing
  • 4.1. Laws of Large Numbers
  • 4.2. Moment Generating Functions
  • 4.3. The Central Limit Theorem
  • Chapter 5. Brownian Motion
  • 5.1. Intuitive Introduction to Diffusions
  • 5.2. The Definition of Brownian Motion* and the Wiener Process
  • 5.3. Approximation of Brownian Motion* by Coin Tossing Sums
  • 5.4. Transformations of the Wiener Process
  • 5.5. Hitting Times and Ruin Probabilities
  • 5.6. Path Properties of Brownian Motion
  • 5.7. Quadratic Variation of the Wiener Process
  • Chapter 6. Stochastic Calculus
  • 6.1. Stochastic Differential Equations
  • 6.2. Itô’s Formula
  • 6.3. Properties of Geometric Brownian Motion
  • 6.4. Models of Stock Market Prices
  • Chapter 7. The Black–Scholes Equation
  • 7.1. Derivation of the Black–Scholes Equation
  • 7.2. Solution of the Black–Scholes Equation
  • 7.3. Put-Call Parity
  • 7.4. Implied Volatility
  • 7.5. Sensitivity, Hedging, and the Greeks
  • 7.6. Limitations of the Black–Scholes Model
  • Endnotes
  • Bibliography
  • Index
  • Back Cover

  • 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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
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