INFORMS Journal on Computing
Vol. 25, No. 1, Winter 2013, pp. BR1–BR10
issn 0899-1499 | eissn 1526-5528 | 2501
http://dx.doi.org/10.1287/ijoc.2013.1.br
c 2013 INFORMS
Book Reviews
Harvey J. Greenberg, Editor
Professor Emeritus, University of Colorado Denver, hjgreenberg@gmail.com
The INFORMS Journal on Computing (IJOC) reviews books on subjects at the interface between operations research and computer science. We welcome books on theory, applications,
computer systems, and generally any subject covered by an IJOC Area, or any combination
of these. This includes both printed and electronic books. In addition, we consider comparative reviews—several books on one relevant topic. Team reviews are also possible, particularly
for a large, broad-scope book, such as an encyclopedia. For further information, please visit
www.informs.org/Pubs/IJOC/Book-Reviews.
In this issue, we review three books. The first uses the paradigm of the traveling salesman
problem to bring the limits of computation to life for algorithm design and analysis. The reviewer,
Gábor Pataki, received his Ph.D. in Algorithms, Combinatorics, and Optimization from Carnegie
Mellon University in 1996. He joined the faculty of the Department of Statistics and Operations
Research, University of North Carolina at Chapel Hill, in 2000. His research is in integer and
convex programming with recent papers on the complexity of the classical branch-and-bound
algorithm, the closedness of the linear image of a closed convex cone, and semidefinite programs
that behave badly from the standpoint of duality. Among his publications, Gábor wrote “Teaching
Integer Programming Formulations Using the Traveling Salesman Problem” [SIAM Review 45-1,
2003], directly applicable to the essence of this book. His review is both informative and insightful.
He concludes, “the next time a student asks me ‘Why are you guys so crazy about research?’, I
will just answer, ‘Read this book.”’
The second book deals with e-commerce. The reviewer, Steve Kimbrough, is Professor of
Operations and Information Management at The Wharton School, University of Pennsylvania.
He is a recognized expert in many things centered around concepts and methods for knowledgebased decision support, including e-commerce. As early as 1997, Steve was invited to be the
keynote speaker at the SOBU Symposium on Electronic Commerce, Tilburg University. His
work with DSS is extensive, including heading up the Coast Guard’s Knowledge-Based Support
Systems project for ten years, as well as several other related sponsored research projects. Within
e-commerce, he has a long, ongoing research stream applying formal logic to business messaging
with the aim of developing a formal language for business communication. His teaching and
research continue to include this growing area, making him eminently qualified to review this
book. Steve points out, “The book focuses on understanding complex, multi-attribute choice
tasks in the online consumer purchasing context.” He concludes, “I believe that this book has its
greatest value as a resource and point of departure for those with an interest in doing research
in this worthy area.”
The third book deals with finance models, which uses Matlab for exercises. The reviewer is
James Morris, Emeritus Professor of Finance in the School of Business at the University of Colorado Denver. After receiving his Ph.D. in Finance from the University of California, Berkeley,
Jim joined the faculty at The Wharton School, followed by a range of visits in the U.S. and
Europe. Joining UCD in 1982, he continued to teach financial modeling and publish in a variety
of journals. During 2006–09, Jim was Director of the UCD M.S.-Finance Program and offers us a
perspective as teacher, researcher, and curriculum designer. He notes that there could be a problem with finance majors in a business school who have insufficient mathematical background and
mathematics majors who have insufficient knowledge of options, but he concludes, “In summary,
Monte Carlo Simulation with Applications to Finance is well done.”
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In Pursuit of the Traveling Salesman: Mathematics at the Limits of
Computation, by W. J. Cook, Princeton University Press, 2011. See
http://press.princeton.edu/. B
Reviewed by: Gábor Pataki, Department of Statistics and Operations
Research, University of North Carolina Chapel Hill, gabor@unc.edu.
How do you find a tour of minimum length that visits each city in a given list exactly once, and
returns to the start? Not just a fascinating mathematical puzzle, the traveling salesman problem
(TSP) finds uses in areas as diverse as logistics, data mining, and computational biology. Its
study has seen remarkable successes in the past 60-odd years. Starting with the optimal solution
of a 49-city USA instance in 1954 by Dantzig, Fulkerson, and Johnson, the current record among
optimally solved instances has 85,900 cities. For the world-TSP with over 1.9 million cities, a
solution proven to be within 0.047% of the optimum is available. These computational successes
were driven by advances in our theoretical understanding of the polytope underlying the TSP, of
approximation algorithms and heuristics.
Bill Cook of Georgia Tech is a leading authority on the subject; his Concorde code, written
primarily with David Applegate, Bob Bixby, and Vašek Chvátal, currently holds the record in
finding optimal solutions to TSP instances. Whereas technical, in-depth treatments of the topic
have been available (see, for instance, [1, 2, 3]), this book is geared to the layperson with a
solid high-school mathematics background. It aims to pique the reader’s interest with the hope
that some will take up research in the area, and deliver a new leap in our understanding of the
TSP. The book’s coverage of the subject is intuitive, and largely geometric, with many excellent
illustrations. There are few equations. Still, there is sufficient mathematical detail to provide a
good start to readers interested in a more technical treatment. The style is congenial, breezy, and
entertaining; many anecdotes and pop culture references are included. Even seasoned researchers
will find the book a truly enjoyable read, and it can serve as an ideal basis for a college level
freshman seminar.
The appetizer of Chapter 1 takes us on a tour of TSP computation from the 1954 study of
Dantzig and his colleagues, through a 1962 Proctor & Gamble challenge with a $10,000 prize, and
to current records. It introduces the reader to the dichotomy between good and bad algorithms
through the concepts of polynomial time computability, NP completeness, and the potential
consequences of finding a polynomial algorithm for the TSP (including the end-of-world scenario
in a 2001 science fiction novel by Charles Stross).
Chapter 2 covers the origins. We learn that actual salesmen (numbering approximately 350,000
in the United States in 1900), traveling judges (among them the young Abraham Lincoln), and
traveling preachers were major consumers of more or less well designed tours. The origins of
the Hamiltonian cycle problem are also treated here, through the Icosian game (a tour-finding
game through the corners of the dodecahedron), and Tait’s incorrect proof of the existence of
Hamiltonian cycles in 3-connected, 3-regular graphs, and its connection to the 4-colour theorem.
After a discussion of the contrast between Hamiltonian cycles and Eulerian tours, we arrive at
the first true mathematical lecture on the TSP (more precisely, on the shortest Hamiltonian path
problem), given by Menger in 1930. The chapter concludes with a review of the famous TSP
constant, and its connection to Mahalanobis’ study on the optimal inspection of jute crop in
1930s India.
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Chapter 3 presents applications, some straightforward (in routing, and logistics), some much
less so: TSP tours help find the optimal movement of telescopes to scan celestial objects and of
laser beams to create artwork; they identify genome orders, create aesthetically pleasing tours of
musical collections, and even help compose music.
Chapter 4 describes heuristics to construct good tours. Starting with the pegs-and-strings
approach employed to find the optimal solution in the Dantzig et al. computation, we are
walked through the nearest-neighbour algorithm and its relatives, Christofides’ heuristic, the
Lin-Kernighan heuristic of 1973, its striking improvement by Helsgaun in 1998, and others. All
presented algorithms were run on a 42-city version of the Dantzig-Fulkerson-Johnson instance;
pictures of the evolving tours provide exceptional illustrations. The chapter finishes with an
overview of ant colony optimization, and genetic algorithms.
Chapter 5 covers the history, geometry, and duality of linear programming, and its use in
attacking salesman problems. It shows how the TSP can be formulated as an integer program;
this is the first place where the subtour inequalities appear. This chapter also contains a nice
coverage of the Jünger-Pulleyblank bounding technique for geometric TSP instances, its relation
to duality, and the 4/3 conjecture on the gap between the subtour LP relaxation and the optimal
tour.
Cutting planes are the subject of Chapter 6, which starts with a step-by-step description of
how Dantzig, and his colleagues proved the optimality of their 49-city tour. Separation algorithms
are then covered for comb inequalities, clique trees, and Letchford’s domino parity constraints,
the latter significantly contributing to the solution of the record 85,900 city instance. Edmonds’
“glimpse of heaven”—his polynomial-time perfect-matching algorithm—follows, and the tantalizing (if unlikely) possibility that a similar algorithm may exist for the TSP; these topics naturally
lead to the equivalence of separation and optimization.
Likening the search for an integral point in a polyhedron to seeking a needle in a haystack,
the addition of cutting planes to removing excess hay, and the process of branching to splitting
the haystack, Chapter 7 presents an intuitive, and well-illustrated history, and description of
branch-and-bound, and of branch-and-cut, the result of its combination with cutting planes.
Chapter 8 charts the progress of TSP computation from 1954 to the present day. As the sizes
of the solved problems increase, each one is accompanied by a fascinating research story. We learn
of the importance of parallel computing (the solution of the record 85,900 city instance took the
equivalent of 136 years of computing on a single machine), and how the Applegate et al. team
provided easy-to-verify proofs of the optimality of its tours. The Mona Lisa TSP, the world-TSP,
and the star-TSP (with 100 thousand, 1.9 million plus, and 526 million plus cities, respectively)
remain the top three challenges. The reader will likely be surprised to learn that the last one,
with the best known solution “only” within 0.419% of optimal, is considered 10 years behind the
world-TSP, for which there is a 0.047% solution available.
What is an algorithm, a “good” algorithm, and the “best” algorithm for the TSP from the
theoretical viewpoint? Chapter 9 delves deeper into complexity theory, starting with the $1 million Clay Institute Prize for settling the P versus NP question. We learn about Turing machines,
and Edmonds’ quest to have polynomial time accepted for “good” in the world of algorithms.
(Those who always took the equivalence of these for granted will be surprised to learn just how
arduous his campaign was.) We are then led through the theory of NP-completeness, and approximability and inapproximability results. A survey of challenges less daunting than deciding
whether P equals NP follows: beating the 60-year old record of Held and Karp’s O(n2 2n ) algorithm, the 3/2 approximation ratio of Christofides’ heuristic and the 220/219 inapproximability
ratio of Papadimitriou and Vempala.
In the future we may end up solving TSPs without “Turing-style” computers; the chapter
ends discussing various other models of computing, such as DNA computing (in vitro and in
vivo), optical, and quantum computing, and even how time travel may get involved. Nonetheless,
Bill concludes that the pegs-and-strings approach from the 1800s (also used by several modern
research groups) would still beat any of these alternative methods.
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Chapter 10 turns to the question of how sentient creatures (humans without recourse to
computers, chimpanzees, pigeons, and the like) solve small salesman problems. All prove to be
remarkably adept. In one experiment, 7-year old children routinely found solutions within 9.4%
of optimal in 15-city instances and the TSP and related puzzles also appear in clinical tests in
psychology. In another study a group sought aesthetic tours and another group, short tours; the
results ended up rather close, with a member of the first team as overall winner. Still, the problem
sizes considered here are small, and no proof of optimality (or near optimality) is supplied by
either children, or pigeons; thus the author concludes that in a man vs machine TSP competition
the computer is likely to come out on top.
“The salesman creating art” is taken up in Chapter 11. The paintings of Julian Lethbridge
and Philip Galanter vividly capture the partitioning of the plane by a salesman tour. Mathematician Robert Bosch employs optimization more heavily in his TSP art: suitable constraints
enforce symmetry of the TSP curve, or that certain pairs of points lie on opposite sides, “bending
the curve to the artist’s will.” In other art pieces, tours or tour-like curves display more complex
images. Artist Eric J. Morales creates striking human portraits from long, meandering, nonintersecting lines. The team of Robert Bosch and Craig Kaplan wields TSP tours to render classical
paintings: the 100 thousand city Mona Lisa TSP and the 140 thousand Birth of Venus TSP are
based on their work. The art of mathematician Jaroslav Nešetřil and painter Jiři Načeradský is
covered next, and finally, we pay a visit to the Bonn Arithmeum, dedicated to computing, art, and
music. The design of VLSI chips can be significantly improved using discrete optimization—the
resulting layouts also give rise to attractive images that form part of the museum’s collection.
Chapter 12 brings the conclusion: the TSP is addictive, as researchers attest, and more than
an ingenious puzzle, or even a practical optimization problem. Unsolvable instances of any NPhard optimization problem are likely to remain. How do we then still push the limits? By pulling
out all stops (a memorable story from Chapter 4 is how Bill and David Applegate wrote a
program that in turn wrote a program to examine 5-opt, 6-opt, etc. tour-improving exchanges.
The output for 8-opt is a 17 million line plus long C-code). Bill advocates adapting this leaveno-stone-unturned attack on the TSP to other problems as well—in other words, the approach
of “bashing on regardless.”
As I mentioned before, the book is ideal for a layperson’s independent study, for an enjoyable
read for just about anyone, and for a first year seminar. Because the chapters are rather loosely
coupled, I think some of them can be used independently to give students a look at topics that
go beyond the main subject of a course. For instance, in an undergraduate course on discrete
mathematics Chapter 5 can serve as a quick and friendly introduction to linear programming;
in an introductory course on optimization (where the TSP may not otherwise be included) one
could devote some lectures to covering parts of Chapters 3 through 8. Finally, the next time a
student asks me “Why are you guys so crazy about research?”, I will just answer, “Read this
book.”
References
[1] D. L. Applegate, R. E. Bixby, V. Chvátal, and W. J. Cook. The Traveling Salesman Problem:
A Computational Study. Princeton University Press, 2007.
[2] G. Gutin and A. P. Punnen. The Traveling Salesman Problem and Its Variations. Kluwer,
2007.
[3] E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, and D. B. Shmoys. The Traveling
Salesman Problem: A Guided Tour of Combinatorial Optimization. Wiley, 1985.
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Interactive Decision Aids in E-Commerce, by Jella Pfeiffer,
Physica-Verlag, 2012. See http://www.springer.com. B
Reviewed by: Steven O. Kimbrough, University of Pennsylvania,
kimbrough@wharton.upenn.edu.
Interactive Decision Aids in E-Commerce is about the design of decision support systems (DSS(s))
for online purchasing decisions. In a prototypical use case, a consumer uses a web browser to interact with a vendor’s site for the purpose of choosing which, if any, available cell phones to buy,
where the items in the consideration set (the phones, etc.) have multiple attributes of interest.
The book was produced as a Ph.D. thesis in Germany and retains multiple references to “this
thesis” and “this dissertation.” The work, however, was undertaken with much real-world motivation and in conjunction with a vendor working in the relevant space (Icosystem Corporation
http://www.icosystem.com). The book is successful in providing a usefully comprehensive (not to
say exhaustive or fully complete) overview of the problem area, in drawing together a great deal
of relevant literature from marketing and behavioral decision-making as well as from information
systems, and in offering new contributions and results.
Readers of JOC with an interest in behavioral decision-making and in DSS, especially those
with an interest in online recommender systems, recommendation agents, collaborative filtering
systems, and multi-attribute decision-making, will find much of interest here, and perhaps a different perspective on the subject. For example, Pfeiffer finds that recommendation agents, once
quite popular, have largely disappeared from the Web, in favor of user interfaces and supporting
systems that facilitate direct choice by users. This development serves to underscore the importance of the general approach favored in the book. The material in the book will be useful to
instructors covering e-commerce, DSS, or behavior decision-making, as well as to researchers in
these areas. The book is not suitable as a textbook, but it may provide valuable services for
a research seminar and as supporting material for teaching. The remainder of my remarks are
addressed to this audience: the reader has an interest in the relevant areas and hence potentially
has an interest in examining the book directly.
It is helpful to begin by listing and briefly discussing a number of key items (concepts, results,
etc.) that serve crucially in the conceptualization in the book. The first of these is the work
related to Payne, Bettman, and Johnson’s The Adaptive Decision Maker[4] (surely the most
cited reference in Pfeiffer’s book by far). Like the present work, this earlier work was concerned
with understanding human decision processes in the context of multi-attributed consumer choices.
This literature looks at, and aims to understand, the various decision strategies (our second key
item) that people employ in these contexts, such as lexicographic ordering, elimination by aspects,
satisficing, and weighted attribute utility modeling. Pfeiffer, quite appropriately, inherits these
decision strategies and seeks to understand both online purchasing behavior and how to design a
DSS in terms of them. (See [5, pages 20–2 and Appendix A] for the full consideration set; there
are 15 in all. Chapter 2 provides a review and discussion of the work related to [4] and of the
various decision strategies. Many of these results are based on MouseLab and experiments with
related systems that have users click for information, or on eye-tracking experiments.)
The third key item or concept on our list is what Pfeiffer calls IIMT (interactive information
management tools). These are essentially fundamental operations that an interactive DSS (called
an interactive decision aid, or IDA) might have to support user choices. There are seven: CAL-
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CULATE, FILTER, MARK, PAIRWISE COMPARISON, SCORE, SORT, and REMOVE. Their
names suffice as descriptions for present purposes (see [5, Table 6.1, page 117] for details). As
Pfeiffer notes, each operation has good justification based on existing literature in DSS, yet not
all of these are present in existing commercial systems. The fourth item is choice task complexity,
which is introduced as follows.
Choice task complexity describes how difficult consumers arrive at decisions. It depends on several factors, such as the amount of product information, the degree to
which the decision maker has to tradeoff product features with each other[5, page 3].
(Note the misplaced modifier in the first sentence. Complexity is meant to apply to difficult
decisions and difficulties consumers have in making them. There is much of this sort of thing in
the book, but on the whole it is quite comprehensible. As someone whose German is not as good
as Pfeiffer’s English, I think we should be very tolerant of such things.) Pfeiffer operationalizes
choice task complexity by what is essentially product similarity on the given attributes, e.g.,
“when products are very similar to each other and when there are a lot of trade-offs” (to be
made because the attribute values are correlated), then choice is complex[5, page 186].
Finally, the fifth essential item we need to frame the work is INTACMATO (INteractive
inforMAtion MAnagement TOol), the DSS that was built and evaluated as part of this work.
Approximately half of the book is devoted to presenting and evaluating this system.
With these items at hand, we can say succinctly and more clearly what the book does. The
book focuses on understanding complex, multi-attribute choice tasks in the online consumer
purchasing context. It seeks to do so in terms of established basic decision strategies (for multiattribute decisions on consumer goods) and it seeks to support and understand such decision
making with and in terms of IIMT (decision operators). To these ends, the book describes empirical studies, one group on context complexity and decision processes (decision strategies and
their uses in Chapter 3) and one on context complexity and final choice (in Chapter 4). Following
this, in Chapters 5–8, the book explores the uses of IIMT in the context of the INTACMATO
system implementation, and undertakes its evaluation. Here are the principle points that arise:
1. The material in Chapter 3 focuses on attribute-wise versus alternative-wise decision making.
Do subjects compare alternatives mainly on an attribute-by-attribute basis or do they
holistically compare complete alternatives with one another? A main finding is that subjects
tend to begin with attribute-wise information gathering and later switch to alternative-wise
choice, after the consideration set has been narrowed. Broadly speaking, the findings and
results are in accord with the prior literature, both in marketing (Payne et al.) and in
information systems.
2. The material in Chapter 4 focuses on uses of the decision strategies. Pfeiffer generally finds
that with increasing complexity subjects shift towards use of non-compensatory strategies
(such as lexicographic ordering and elimination by aspects) and away from the more normative strategies, such as linear utility functions. These results are also in reasonable accord
with the prior literature.
3. Part II, Chapters 5–8, addresses implementations of DSS (IDA in Pfeiffer’s terminology).
Distinction is made between recommendation systems, some kinds of which are prominent
on the Web (think: Amazon’s “More Items To Consider” and “Customers Who Bought
This Item Also Bought”) and IIMT systems, which aim to support individuals in making
choices from a consideration set. Some empirical evidence is brought to bear in favor of the
IIMT approach, but mostly the focus is on evaluating the INTACMATO implementation.
Evaluation is in terms of perceived ease of use, perceived usefulness, confidence, shopping
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enjoyment, and satisfaction. As usual, the established literature is the source of the criteria
and the book documents this well.
The final chapter, Chapter 9, discusses the study overall and addresses the practitioner community, that is vendors who sell complex, consumer goods on the Web. Perhaps the main takeaway proffered is the finding (developed throughout the book) that users will often switch decision
strategies during their decision processes. Typically, they will engage in rough screening at the
start and focus more deeply on a few options at the end. Thus, suggests Pfeiffer, offering flexible
IIMT-based DSS makes a lot of sense.
To conclude, I believe that this book has its greatest value as a resource and point of departure
for those with an interest in doing research in this worthy area. Although the experiments are
carefully considered and a very extensive literature is canvassed, it is fair to conclude that while
much has been learned, little is yet settled scientifically. (I am referring to the entire literature,
not just Pfeiffer’s contributions, and I see this as a point of encouragement for researchers.)
Where to go next in this important and very complex area? I’ll suggest just one direction by way
of illustrating the general point.
While it is interesting to know what users like, that by itself leaves open prescriptive questions,
and in particular questions about decision quality and commitment. On the commitment side,
we might look at the kind of design found in [3], where different utility assessment methods were
compared by seeing whether subjects would stick with them or violate them in the case of a
difficult choice. When real money is on the line, which methods do subjects trust more? On the
quality side, concomitant with complexity in Pfeiffer’s sense will likely be smaller differences in
overall utility. Complex choices are harder because the options are closer in value, and less easily
distinguished. One would like to know whether simple heuristics that make us smart (e.g., [1, 2])
might not garner some prescriptive force and merit inclusion in future DSS.
References
[1] G. Gigerenzer and R. Selten. Rethinking rationality. In G. Gigerenzer and R. Selten, editors,
Bounded Rationality: The Adaptive Toolbox, pages 1–12. MIT Press, Cambridge, MA, 2001.
[2] G. Gigerenzer, P. M. Todd, and ABC Research Group. Simple Heuristics that Make Us
Smart. Oxford University Press, New York, NY, 2000.
[3] S. O. Kimbrough and M. Weber. An empirical comparison of utility assessment programs.
European Journal of Operational Research, 75:617–633, 1994.
[4] J. W. Payne, J. R. Bettman, and E. J. Johnson. The Adaptive Decision Maker. Cambridge
University Press, Cambridge, UK, 1993.
[5] J. Pfeiffer. Interactive Decision Aids in E-Commerce. Physica-Verlag, A Springer Company,
Heidelberg, Germany, 2012.
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Monte Carlo Simulation with Applications to Finance, by Hui Wang,
Chapman & Hall, 2012. See http://www.crcpress.com/. B
Reviewed by: James Morris, University of Colorado Denver,
James.Morris@ucdenver.edu.
Monte Carlo Simulation with Applications to Finance provides the reader with an introduction
to the mathematics of option pricing and a guide to Monte Carlo simulation of option prices.
The author, Hui Wang, Associate Professor in the Department of Applied Mathematics at Brown
University, says the book can serve as a one-semester course on Monte Carlo simulation, with the
intended audience consisting of advanced undergraduate or masters students who wish to learn
about this subject.
The book is relatively short, consisting of ten chapters in 280 pages. The first three chapters
reviews probability, introduces Brownian motion, and explains the idea of arbitrage-free pricing,
respectively. Chapter 4 explains the ideas and mathematics of Monte Carlo simulation. Chapters
5 through 7, along with Chapter 9, deal with methods of sampling in Monte Carlo, reduction
of variance of simulated estimates, importance sampling, and simulation of continuous diffusion
processes. Chapter 8 provides an overview of stochastic calculus relating to security prices and
options, and Chapter 10 is concerned with simulating the sensitivity of the option price with
respect to parameters such as the stock price, the interest rate, time to expiration of the option,
and the volatility of the stock return (the so-called ’Greeks,’ due to the use of Greek letters
to denote these sensitivities in the option literature). Each chapter has examples in the text,
and has problems at the back of the chapter. MATLAB is the language used for executing the
simulations, and MATLAB code is shown for many of the examples in the chapters.
The end-of-chapter exercises are divided into “Pen-and-Paper Problems” and MATLAB Problems. The pen-and-paper problems are mainly exercises in deriving formulas relating to the distributions of security prices and valuation of options. They provide the students with useful practice
that helps them understand the mathematics of security and derivative prices. The MATLAB
Problems, as the title suggests, have the students use MATLAB to model options and to program
Monte Carlo simulations of security and option prices. Both types of exercises are appropriate
and can be useful practice for the reader. However, a major weakness of the book is that it does
not include an instructor’s manual or any sort of solutions for these exercises. It could be difficult
for a student to know when he/she is on the right track unless he/she can see the correct solutions. In addition, some instructors could find the book difficult to teach from without some help
in this regard, and without some sort of guide, the book would be hard to use for the intrepid
individual who wants to use it for self-instruction in simulation. Because this is a text about
Monte Carlo simulation, the heart of the book is Chapter 4: Monte Carlo Simulation. The author
states that “Monte Carlo simulation is a very flexible tool for estimating integrals and expected
values.” There is nothing wrong with the statement as far as it goes. However, I think it tends
to focus too heavily on expected values, with insufficient emphasis on the other reasons we use
Monte Carlo simulation, such as understanding the variability and risks in security markets. One
of the most important reasons for using Monte Carlo is to model the variability so we can understand the risks and have some idea of how wrong we might be. There does not seem to be much
discussion of these aspects. In this chapter and most of the others, the author provides examples
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for simulating option prices along with the MATLAB code for the problem. Then, typically he
shows a table of the results that compare the simulated mean option value with that calculated
with the formula, such as the Black-Scholes model. The standard error from the simulation is
shown, but most of the discussion relates to the simulated mean. Not only is the error in the
simulation important, but the other parameters and characteristics of the distribution of simulated outcomes may be crucial. We may start with a two-parameter distribution as input, but
that does not always mean the output will be of the same type, and knowing just the mean and
standard deviation of the simulated distribution may not be sufficient. In this regard, seeing a
picture of the simulated results can be invaluable. There are almost no graphs in the book, and
graphs of the simulated outcomes could really help the student to understand simulation and the
practitioner to better understand the risk and errors of the investments.
With Chapter 4 on Monte Carlo simulation being the main introduction to the subject of
the book, most of the subsequent chapters are devoted to issues of implementing the simulations
and methods for correcting the shortcomings in the simulation. Chapter 5 covers techniques for
generating the sample of random numbers that are input to the simulation. Chapter 6, Variance
Reduction Techniques, covers methods for more efficient sampling to decrease the standard error
of the parameter estimate with fewer samples in the simulation.
Chapter 7 covers importance sampling for problems that deal with very low-probability events,
and presents various algorithms for obtaining estimates. The author notes that importance sampling is a topic more advanced than this text. Nevertheless, this is the longest chapter in the
book. Chapter 9 deals with methods for correcting biases when a continuous process is simulated
with a discrete process.
These middle chapters are the bulk of the book and are clear and well done, but they seem
more suited to students who have previously worked with Monte Carlo simulation and need this
material to handle more advanced problems. The student who is just being introduced to the
application of Monte Carlo to option pricing would benefit from a more step-by-step explanation
of Monte Carlo methods before seeing these more advanced topics. That is, the book would
be improved by adding more explanations and examples in the introduction to Monte Carlo
(Chapter 4) before getting to the more difficult topics that make up so much of the book.
I thought the strongest parts of the text were those chapters that explained the mathematics
of security and option pricing, including Chapter 2: Brownian Motion, Chapter 3: Arbitrage Free
Pricing, Chapter 8: Stochastic Calculus, and Chapter 10: Sensitivity Analysis. Chapter 2 models
the path of security prices as a geometric Brownian motion, and presents the Black-Scholes model
of option prices. This chapter provided a relatively clear review of the mathematics. The weak
point is that a student who has not been previously introduced to options will have a difficult
time understanding the concepts of options. This weakness is partly solved in Chapter 3, which
uses the Cox, Ross, and Rubinstein binomial model to demonstrate how arbitrage yields the
option-pricing models. The presentation is clear and will help the student to understand the
ideas behind option pricing.
Like these other chapters, Chapter 8 provides a good review of its topic. However, stochastic
calculus is at the heart of continuous-time security and option pricing, so I wondered why it is
presented toward the end of the book when it seems like it fits best with the chapters on Brownian
motion and arbitrage free pricing. If I were teaching from this text, I would cover this material
early in the course. Chapter 10 is concerned with the question of how sensitive option-prices
are to variations in the inputs (the Greeks), such as the level of the stock price, the variance of
stock prices, interest rates, and time to expiration of the option. The sensitivity to the Greeks
is explained fairly well, but the student would benefit from some further explanation and more
examples. And, like Chapter 8, it would help the student to be exposed to these concepts of
Greek sensitivity earlier in the text.
Greenberg, ed.: Book Reviews
c
INFORMS Journal on Computing 25(1), pp. BR1–BR10, 2013INFORMS
BR10
I liked this book because it gave me a good review of the mathematics of option pricing.
The chapters are well written and were clear to me. I have taught finance for over forty years at
both the undergraduate and graduate levels, including Ph.D. courses that covered options and
stochastic calculus. So the material was clear to me and the topics were interesting. However,
there is a caveat in the statement that it was “clear to me.” In spite of its intended audience
of advanced undergraduates or students in masters programs, I have doubts about whether the
content and level of the book are consistent with the intended audience.
If the targets are the mathematics students, I doubt that, without other prior courses in
finance and option pricing, they would have a very good understanding of what options are and
would not follow some of the discussion of option pricing. Sure, they can understand the basics of
the formulas, but they probably would not have much intuition about option markets or why we
are concerned with option pricing. On the other hand, the finance students would have a better
understanding of the functioning of the options markets and the basics of option pricing, but
most would not be able to follow the mathematics. Graduate students in many of the financial
engineering programs, where they have strong backgrounds in mathematics and finance, would
probably be able to benefit from both the mathematics and the discussion of option pricing.
In summary, Monte Carlo Simulation with Applications to Finance is well done, but it is
most useful for a select audience as noted above. Less advanced students, particularly in business
programs where they do not have sufficient mathematics background might find some of the
many texts on options and simulation more accessible. Two good examples include Wayne Winston, Financial Models Using Simulation and Optimization II, Palisade Corporation, 2001 and
Dessislava Pachamanova and Frank Fabozzi, Simulation and Optimization in Finance + Website: Modeling with MATLAB,@Risk, or VBA, John Wiley & Sons, 2010, which was reviewed in
this journal.[1] However, these books do not have the mathematical rigor that is present in Hui
Wang’s book.
References
[1] A. Consiglio. Review of Simulation and Optimization in Finance: + Website: Modeling with
MATLAB, @Risk, or VBA, by D. A. Pachamanova and F. J Fabozzi, John Wiley & Sons,
2010. INFORMS Journal on Computing, 24(1):BR1–BR3, 2012.
Books Pending Review
A. Borzı́ and V. Schulz. Computational Optimization of Systems Governed by Partial Differential
Equations. SIAM, 2012.
C. C. McGeoch. A Guide to Experimental Algorithmics. Cambridge University Press, 2012.
E. Schlogl. Quantitative Finance: An Object-Oriented Approach in C++. CRC, 2012.
A. Ray and A. Raval. Introduction to Biological Networks. CRC, 2012.
S. Das. Computational Business Analytics. CRC, 2013.
B. P. Zeigler and H. S. Sarjoughian. Guide to Modeling and Simulation of Systems of Systems.
Springer, 2013.