SCIENCE OF INEXACT MATHEMATICS

Mathematician and consultant Shestopaloff thoroughly explores the world of financial mathematics in a volume that will be valuable to anyone in the field.

Beginning with interest and considering annuities, mortgages, and investment and risk measurement methods, Shestopaloff uncovers the complexities of investment mathematics with clear, understandable text accompanied by numerous derivations, examples, graphs and tables. Topics studied include the internal rate of return–which the author considers in a lengthy discussion that includes its relationship with similar calculations–and nominal and effective interest rates. He also considers compounding using various computational methods and linking–a more accurate alternative to geometric linking, which is applied to financial trading. Shestopaloff discusses measurement of risk with details of the various risks and quantifying methods that are involved in investing, such as risks in interest rate, volatility, operational risk, downside risk and more. He briefly explains the probabilistic calculations involved. The introductory text includes definitions of all terms and rapidly advances through equations to allow mathematicians of different skill levels to follow the explanations. An associated software package is available, and the author briefly reviews computation methods, as well as the accuracy obtained by different methods. Shestopaloff ends with a caution that–although software may make many of these calculations invisibly and easily–it is still imperative to understand the mathematics behind the software. His explanations are thorough without excessive wordiness and the text smoothly accompanies equations and derivations. The author helpfully analyzes business consequences alongside the mathematics. The detailed index and table of contents, with paged references to subtopics, make this a very convenient reference book. Although additional editing could have corrected minor linguistic issues, readers will find the text easy to comprehend. Shestopaloff has presented many of these topics in previous peer-reviewed journal papers, but academics, students and professionals–from programmers to financial mathematicians–will find this a convenient one-volume guide, well-written and seamless.

A valuable addition to the financial mathematician’s library.