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

Steven R. Dunbar
Publication Date: 
Number of Pages: 
AMSS/MAA Textbooks
[Reviewed by
Andrzej Sokolowski
, on
Mathematical modeling represents a rapidly growing area of applying math concepts to build models of systems’ behavior. While its applications in sciences are wide, this book focuses on mathematical modeling in economics and finance. As such, it can serve as a textbook for an alternative course for students in economic sciences. The uniqueness of this book is rooted in merging several different areas of mathematics and robust quantitative reasoning. The reader will find modeling with probability, stochastic processes and difference and differential equations all embraced in the contexts of economics and finances. This merging results in the development of techniques suitable to investigate contemporary financial instruments that are not typically discussed in textbooks. By integrating various areas the author of Mathematical Modeling in Economics and Finance, Probability, Stochastic Process, and Differential Equations 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.
While there are many textbooks and monographs on mathematical finances, this book differs by:
  • Concentrating on modeling processes not on the financial instruments. 
  • Explaining the details of modeling, it can serve as an introductory preparation for more advanced texts.
  • Being applicable to a wider audience because it includes not only the practice of modeling but also post modeling analysis and criticism.
  • Offering a wide span of modeling techniques from the simplest binomial option model to the Black-Scholes-Merton model.
The book is composed of 7 chapters. In chapter 1, Dunbar brings forth the history of mathematical finance and describes in details the scheme of mathematical modeling that he employed the following chapters. A detailed and very clear elaboration on the processes of transferring hypotheses into mathematical structures, Dunbar invites the reader to immerse themselves in the book context and explore. The chapter sections are initiated by starter questions that trigger the reader’s thinking and serve as catalysts to develop chapter contents. Dunbar clearly explains the definitions and notations applied in each chapter and extracts key concepts and vocabulary that makes the textbook a self-contained resource. Extensive diversity of mathematical representations such as algorithms, scripts, graphs, and simulations make the textbook a valuable learning tool. Each chapter concludes with conceptual and numerical problems that provide opportunities for the reader to apply the accumulated knowledge to model new situations.


 Andrzej Sokolowski is a researcher interested in applying mathematical modeling to develop scientific inquiry. 

See the publisher's web page.