Robert R. Reitano has written an ambitious and beautiful book with the aim of creating a new breed of quantitative finance professionals (“quants”) with a deep understanding of the underlying mathematics. As he writes in the introduction, in practice, “standard results may or may not apply, and the most critical job of the finance quant is to determine if the traditional approach applies, and if not, to develop an appropriate modification or even an entirely new approach. In other words, for today’s finance quants, it has become critical to be able to think in mathematics, and not simply to do mathematics by rote.”
Each chapter of this book corresponds roughly to mathematical material covered in a one semester course, but with emphasis on developing only those ideas needed for success in investment finance. There is enough material in this book for many course design options at the level of a first year graduate course in quantitative finance.
My one complaint about many books on applications of mathematics, including this one, is that applications are almost always deferred to an “applications” section or sections at the end of each chapter, rather than being woven into the exposition throughout. Given that one of Reitano’s aims in writing this book is to ensure that the mathematical ideas are rigorously presented and understood by a wide range of students, however, this style may have been the best organizational method.
As someone with a mathematical background changing careers into where quantitative finance knowledge and skills are a must, I found this book a thrill to review — it is very rich in material and I will be studying it for some time to come. Those seeking a career as a quant and not studying the book as part of a standard academic program that covers the programming skills necessary to implement the models and ideas presented in this book are well advised to gain such know-how.
There is a future title planned, Advanced Quantitative Finance: A Math Tool Kit, that will cover more advanced mathematical topics used for investment modelling, derivative pricing, and risk management. I look forward to that title. Until then, I had better get back to mastering the contents of the present volume!
Marcus Emmanuel Barnes is a professional problem solver, lover of mathematics books, and co-creator of Wearmath.com: “Mathematics t-shirts for mathematicians by mathematicians!” You can find out more about what Marcus is currently working on by visiting his personal website at marcusebarnes.com.