Mathematical-tools

If you are in a situation like me, then this might be the best book. I read some introductory long ago at university. A few years from now I needed to refresh on the subject and get a little deeper. I have browsed or read some other books, but this is now my number one choice for reference. It starts very gently with e.g. spelled out examples on matrix addition. It ends with (by my standards) advanced topics like eigenstructures, quadratic forms, generalized inverses etc. I admire the writing style which is compact, precise and at the same time a little relaxed.

There are a lot of people out there who do statistical analysis but who do not possess the mathematical knowledge underpinning a lot of what they are doing (i.e., linear algebra and some calculus). Most of the time people can get away with using stastical software as a sort of 'black box' and not worry about the math. But there are situations when having the background knowledge is crucial.

This book does an excellent job of facilitating self-study of the math underpinning multivariate statistical analysis ... namely, linear (matrix) algebra and some calculus. Each chapter has a set of questions and ALL of the answers are provided in the book (handy for self-study). The one slight critique of this book I can give is that I wish the book did more on the calculus aspects. However, that is a minor comment and the knowledge that this book imparts of linear algebra to self-learners is extremely valuable.

This is a great little book. I would put it in my category of 'original' books on quant finance, which includes books written by Paul Wilmott, Mark Joshi, Rick Osband and Neftci.

The reason being that the author uses a more informal style than most quant books and is very hands-on. If you're interested in understanding quant models and eventually applying them in the real world, then this is the kind of book you want. If you're looking for mathematical beauty and formalism, then look elsewhere.

The editors could have done a better job with some of the flow and formatting - maybe next edition (it is sometimes hard to link the text to the figures and tables).

Great book.

Consider first, this book's subtitle, "Tools for Incomplete Markets." A "complete market" (the kind assumed by the Black-Scholes-Merton model) is one in which any derivative product can be dynamically replicated by means of cash and the underlying asset. An incomplete market, then, is one is which the world of derivatives and their underlyings do not match each other in the point-by-point replicable manner implied by that definition of completeness. This failure to match makes for a necessary imperfection in hedging. That, of course, is the real world, where traders practice, as Scholes and Merton famously discovered in Greenwich, CT not long ago!

A variety of illustrations of this practical emphasis might be adduced. In the preface, for example, Dr. Cerný tells us frankly that in his experience "is it hard to understand the Itô calculus, but it is possible to get used to it and to apply it quickly and consistently...." [italics in original.]