Petters, Arlie O.; Dong, Xiaoying An introduction to mathematical finance with applications. Understanding and building financial intuition. (English) Zbl 1348.91002 Springer Undergraduate Texts in Mathematics and Technology. Cham: Springer (ISBN 978-1-4939-3781-3/hbk; 978-1-4939-3783-7/ebook). xvii, 483 p. (2016). The book is an undergraduate textbook in mathematical finance with applications. In spite of the fact that there are many textbooks in mathematical finance, this textbook has its own advantages, theoretical, pedagogical and applied, to name a few. One of them is a good balance between mathematical description and practice in applications: the book contains numerous examples and exercises that support theoretical derivations and conclusions. The second advantage is that this book is self-contained and no background in finance is assumed: the development is going smoothly from simple interest models to more advanced stochastic calculus and pricing of derivative securities. The third advantage is that this textbook is useful and helpful for students preparing for higher level study in mathematical finance or study in actuarial science.The chapters of the textbook are organized gradually and naturally into four parts: Part I, containing Chapters 1 and 2, introduces to securities markets and interest rates theories; Part II, containing Chapters 3 and 4, describes Markowitz portfolio theory, capital market theory and portfolio risk measures; Part III, with Chapters 5 and 6, models underlying securities using binomial trees and stochastic calculus; Part IV, with Chapters 7 and 8, deals with derivatives securities, Black-Scholes-Merton model, and Merton jump-diffusion model.The textbook is aimed at advanced undergraduates, and also at master’s degree students who want a more rigorous treatment of the mathematical models in finance. This text will be a very good textbook for a year-long course on introductory mathematical finance. Reviewer: Anatoliy Swishchuk (Calgary) MSC: 91-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance 91Gxx Actuarial science and mathematical finance 91B30 Risk theory, insurance (MSC2010) 91B70 Stochastic models in economics 60H30 Applications of stochastic analysis (to PDEs, etc.) 62P05 Applications of statistics to actuarial sciences and financial mathematics Keywords:financial markets; interest rates; Markowitz portfolio theory; capital market theory; portfolio risk measure; binomial trees; security pricing modelling; stochastic calculus; geometric Brownian motion; derivatives; forwards; futures; swaps; options; Black-Scholes-Merton model; European option pricing PDFBibTeX XMLCite \textit{A. O. Petters} and \textit{X. Dong}, An introduction to mathematical finance with applications. Understanding and building financial intuition. Cham: Springer (2016; Zbl 1348.91002) Full Text: DOI