Mathematical Techniques in Finance: Tools for Incomplete Markets (Second Edition)

Mathematical Techniques in Finance ranks as one of the best finance texts I've ever read. This book provides a good mix of theory and application which is well-suited for a master's level course and for practitioners. It fills the gap between undergraduate/MBA finance texts that focus on applications and Ph.D.-level texts that are in the theorem-proof style. To appreciate this book, I think the reader only needs to know calculus and a little linear algebra. The author is able to describe complex mathematical techniques in relatively easy, understandable terms. More importantly, the author highlights the important things to remember for each of the important concepts. For example, whether the absence of a Type I or Type II arbitrage is necessary for the existence of a solution when markets are complete or incomplete or which state variables play an important role in certain models. Moreoever, I have read many finance books, and this text's discussion of risk-neutral pricing and continuous time finance is one of the best. Aside from providing proofs for the more important concepts, Cerny also provides many numerical examples and MATLAB code (the MATLAB programs are available on the author's website) to implement many of the examples.