 
Reviews
SCIENCE
OF INEXACT MATHEMATICS
Investment Performance
Measurement.
Mortgages and Annuities.
Computing Algorithms.
Attribution. Risk Valuation
Midwest Book Reviews (Oregon,
WI, USA)
For dedicated
mathematicians, there is as much art and beauty as there is science in
their calculations, formulas, precepts, concepts, and expositions. There
is also utility, practicality, insight, and value in the application of
mathematical principals to financial systems and the economy which are
complex compilations of factors that mathematicians develop models to
explain otherwise inexplicable and seemingly random phenomena. That's
why Yuri Shestopaloff's "Science of Inexact Mathematics: Investment
Performance Measurement, Mortgages and Annuities, Computing Algorithms,
Attribution, Risk Valuation" is such a seminal work in the field of
applied mathematics to financial issues and economic performances with
respect to investment strategies and interpretations. Offering detailed
computing algorithms (including software implementation), the informed
and informative text is enhanced with numerical examples, graphical and
tabular illustrations throughout. A work of impressive scholarship, Yuri
Shestopaloff's "Science of Inexact Mathematics" is especially
recommended for academic, governmental, and professional library
collections and is a valued contribution as a graduate level mathematics
curriculum supplemental resource. 
ForeWord Magazine
Business & Economics.
SCIENCE OF INEXACT MATHEMATICS: INVESTMENT PERFORMANCE MEASUREMENT,
MORTGAGES AND ANNUITIES, COMPUTING ALGORITHMS, ATTRIBUTION, RISK
VALUATION by Yuri K. Shestopaloff (AKVY Press, 592 pages,
hardcover, $89.95, 9780980966701): Doctor of Sciences and author of
Sums of Exponential Functions and their New Fundamental Properties
and more than eighty academic articles on mathematical modeling presents
a comprehensive monograph on investment analysis, introducing new
methods and unifying existing ones within a single conceptual framework;
the book ranges from its theoretical underpinnings to the software
implementation of particular algorithms, e.g. for the fast computation
of the Internal Rate of Return. 
Kirkus Discoveries,
Nielsen Business Media, 770 Broadway, New York, NY
10003, discoveries@kirkusreviews.com
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
peerreviewed journal papers, but academics, students and
professionals—from programmers to financial mathematicians—will find
this a convenient onevolume guide, wellwritten and seamless.
A valuable addition to the
financial mathematician’s library. 
Zentralblatt
MATH Database 1931 – 2009, c 2009 European Mathematical Society, FIZ
Karlsruhe & SpringerVerlag (Berlin, Germany)
Zbl pre05526839
Shestopaloff,
Yuri K.
Science of
inexact mathematics. Investment, performance, measurement.
Mortgages and
annuities, computing algorithms, attribution, risk valuation.
(English)
Toronto: AKVY
Press. 591 p. EUR 69.95; $ 89.95; £ 69.95 (2009). ISBN 9780980966701/hbk
The book
presents a coherent and comprehensive study of mathematical methods for
investment performance measurement, attribution analysis, mortgages,
annuities and
investment risk
measurement. Mathematical backgrounds are comparatively simple, so the
book can be useful both for academic studies and for practitioners. It
consists of 11 chapters.
In Chapter 1 the
wellknown Internal Rate of Return (IRR) equation for cash flows with
fixed compound interest rate is derived and discussed. The applications
of this equation
to annuities and
mortgages are considered in the Chapters 2 and 3. Chapters 4 and 5 are
devoted to the calculation of rate of return and solving IRR equation.
Computational
efficiency of
algorithms for solving IRR equation is discussed on Chapter 6. Chapter 7
proceeds with a conceptual level in understanding rate of return.
Influence of negative
cash flows,
extreme scenarios with large cash flows, modified IRR method are
studied. The new linking algorithms for investment performance
measurement and trading are
introduced in
Chapter 8. Chapter 9 and 10 are devoted to investment attribution
analysis and measuring risk, correspondingly. Chapter 11 contributes to
the problems
of “real”
calculations: solutions’ quality, applicability domains, some specific
features of financial industry.
Keywords :
internal rate of return; lending and investment; annuities; investment
performance
measurement;
attribution models; modified Dietz equation; risk measurement
Classification :
9101
Instructional exposition (Social and behavioral sciences)
91B28 Finance etc. 
Library
of Congress, USA
Science, Tech and
Business recommender wrote about books by Yuri K. Shestopaloff the
following (“Sums of exponential function and their new fundamental
properties” and “Science of inexact mathematics”): “Both titles are very
impressive academic works and the Library is very pleased to acquire
these publications for inclusion to the collections” 
Dr.
Wolfgang Marty, Vice President of CREDIT
SUISSE, Zurich,
Switzerland
As I have
worked in numerical analysis and in the banking industry, I think that
the book adds great value to the area of performance measurement. The
concepts are introduced with mathematical precision accompanied by
thorough descriptions. I found many issues addressed for the first time.
As an example, the role of the NewtonRaphson iteration and similar
methods for computing the internal rate of rate are illustrated in
detail. Generally, the importance and power of mathematical methods in
performance measurement is greatly emphasized. The book adds value to
indepth portfolio analysis, because return and risk considerations are
in the centre of the material presented. This book is a must for every
professional in the finance industry. 
Sergei Beliaev, Former
Director of Department developing Investment Performance Measurement
Systems at Royal Bank of Canada
I knew the author
as a system architect, when he was designing an investment performance
measurement system for the Royal Bank of Canada. (That time, I was a
Director of this department.) In this review, I am looking at the book
from the perspective of a system designer, one who has to understand all
related mathematics to implement the system. I wish we had this book
when we were developing our investment performance measurement systems.
All the answers we were looking for are in this book, and even more. At
the outset, we lacked an understanding of relationships between the
different types of rates of return. The book completely covered this
subject. We also did not know which computational algorithms are better
and how they compared to each other in terms of performance, accuracy,
etc. This book covers this information indepth and is in itself a
treasure trove for system designers. There is an interesting chapter on
attribution analysis. The author covers all available methods and in
addition, introduces a framework and develops new methods on his own,
with impressive numerical results. I would also pay attention to new
linking methods named in the literature for author. These are very
valuable methods from a systems development perspective. Asset and
period “slicing and dicing”, “asset schemas”, etc. are always a headache
for system designers complicating things immensely, and this is
something that these methods solve. Overall this book is a must have for
any serious systems designer or performance measurement analyst. 
5.0 out of 5
stars
Useful for beginners and professionals, August 23, 2009, Review from
Amazon.com
A.
Sharikov (LA, USA) The author calls this manuscript a
reference book. This is true, because beginners who specialize in the
given area will find accurate definitions, necessary formulas for
compound and noncompound use cases, many illustrations and practical
examples of calculations of internal rate of return.
For the wider public, the book will be useful as good reading about the
pitfalls of calculating internal rates of return when simple
noncompound formulas are used to simplify calculation instead of more
accurate compounding approaches.
On the other hand, professional practitioners will find analyses and
examples on the implementation of numeric methods and computer
algorithms, including a comprehensive firsthand explanation of
Shestopaloff's linking (SL) method from its author.
SL allows one to combine internal rates information about different
investment periods to find total rate of return. The method can be used
to link sequential and nonsequential periods.
The author shows the relationship between SL and wellknown geometric
linking and how SL extends the geometric linking approach.
The author compares the results of all algorithms available today to
prove SL effectiveness.
I found interesting the discussion of the important role of modified
Dietz formula and its usage in numeric calculation.
The book describes different mathematical aspects of annuities,
mortgages, the internal rate of return equation, investment attribution
analysis, and risk assessments, and can probably be used for the
development of new trading techniques. 
5.0 out of 5
stars, Review from Amazon.com,
by Angel In my view, the pros
are the comprehensiveness and depth of the subject coverage; a
consistently scrupulous level of detail; flawless clarity of
presentation. What appeals is that the reader can start from scratch and
get to an advanced level in all areas of investment performance
measurement just by reading this one book, in parts or as a whole. The
volume combines the qualities of a reference book, well thought through
and conceptually seamless monograph, and a handy manual, when it comes
to practical application of investment performance methods and
computational algorithms. All in one book! As a note, the computational
and system implementation parts are unique, both with regards to the
subject itself and, again, in the comprehensiveness of coverage. System
designers should be happy to have this book when designing financial
systems. Financial analysts, like myself, will benefit in all aspects of
business knowledge. The good thing is that the book will be uptodate
for a long time, the depth of conceptual thinking that it presents will
unlikely change for decades. I am not sure that all people need the
small occasional insertions of general considerations, some of them
almost of a philosophical level. Personally, I found some of them
interesting. However, this is a minor thing. This is not that these
insertions should not be there. They are just not for everybody.
Otherwise, the book is an excellent buy. 
