Mathematical Methods for Financial Markets provides a comprehensive overview of mathematical research inspired by financial markets, primarily derivative-securities markets. The authors have tried to strike a balance between financial concepts and mathematical considerations; the balance, however, skews heavily towards the mathematics. Mathematicians interested in finance who are trained in the theory of stochastic processes can find much of interest here.
The book is labeled a “textbook” and the introduction suggests the book will be of use to practitioners in the financial field. I do not agree with either statement. The book is more a monograph than a textbook. There are 650 notationally dense pages with very little exposition, 50 pages of references, and seven(!) illustrations, none based on data. The book is deliberately not self-contained, with many details being loaded off on the references. Furthermore, the sections have an intricate dependency, so that many sections refer to and rely on concepts that will be introduced later in the book.
I cannot see how this book could be used for instruction, except via the dreadful phrase “you might want to have a look at this book.” There is a smattering of exercises, but they are not appropriate for practitioners. I could argue this point at length, but a practitioner looking at the book will notice that nearly every exercise contains the word “prove” and know the game is up.
Financial considerations are secondary in this book, because the authors take for granted that financial markets can be modeled by stochastic processes, and thus they need discuss only stochastic processes. As they note in the introduction, concerning the “financial crisis (2007–?)… Revisiting previous axioms in such a changed situation is a huge task… However, for obvious reasons, our book does not deal with these new and essential questions.” Indeed, changing the models for financial markets could make much of stochastic process theory irrelevant.
John Curran is Associate Professor of Mathematics and the coordinator of the Actuarial Science and Economics Program at Eastern Michigan University.