Mathematics and Tools for Financial Engineering [Bookshelf]

As the title of this monograph describes, the book has two major aims: 1) to present the mathematics that are used for financial engineering and 2) to provide the financial tools that are necessary in the study of financial engineering. The mathematics presented here are very thoughtfully selected from different areas and serve to demonstrate the interdisciplinary character of the financial engineering field. The mathematics part of the book surveys elements of set theory, linear algebra, real analysis, approximation and numerical analysis, optimization theory, probability theory, and stochastic processes. The selection of the elements of several areas of mathematics (with each topic typically being taught in a dedicated semester-long course) is a tough challenge and requires teaching experience. It is obvious to this reviewer that the book is written based on the author’s experience in teaching this course. The mathematical part emphasizes topics of linear algebra, including matrices and their operations, linear equations and methods for solving systems of linear equations, computing the inverses of matrices, and determining eigenvalues and eigenvectors. While these topics can be obtained in a basic course in linear algebra, the succinct presentation of this material in this book enhances the success of communication of these ideas. The mathematical tools part of the book continues with the study of optimization of functions and then stochastic processes. Again, while all of these mathematical topics are clearly available elsewhere, the author has condensed them into a very readable account.