The most recommended books about mathematical models

Who picked these books? Meet our 20 experts.

20 authors created a book list connected to mathematical models, and here are their favorite mathematical model books.
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Book cover of Theory of Value: An Axiomatic Analysis of Economic Equilibrium

Thijs ten Raa Author Of Microeconomics: Equilibrium and Efficiency

From my list on microeconomics on how markets are interconnected.

Why am I passionate about this?

Microeconomics is a turnoff to most readers. Not without reason. Many books in this field are dull rewrites of other books and opaque.  In particular, it is not clear how the behavior of individual consumers and producers adds to the performance—good or bad—of an economy. The books listed here helped me to sharpen my own mind and to make my writing lucid.

Thijs' book list on microeconomics on how markets are interconnected

Thijs ten Raa Why did Thijs love this book?

As a math student I found economics a slippery subject and, therefore, was hesitant to read any book on the subject. 

Theory of Value is a short, formal manuscript, that includes the definition of an economy. It was the first book I read in economics and I loved it. It induced me to move to New York and to study the field.


By Gerard Debreu,

Why should I read it?

1 author picked Theory of Value as one of their favorite books, and they share why you should read it.

What is this book about?

"[This] beautiful and austere book . . . [is] an important landmark of economic theory."-F.H. Hahn, Journal of Political Economy
"An immortal classic of twentieth century economics. Every economist should own a copy."-Robert Lucas, University of Chicago
Theory of Value offers a rigorous, axiomatic, and formal analysis of producer behavior, consumer behavior, general equilibrium, and the optimality of the market mechanism for resource allocation.


Book cover of Technical Analysis of the Financial Markets: A Comprehensive Guide to Trading Methods and Applications

Alan Northcott Author Of Mastering Technical Analysis: Strategies and Tactics for Trading the Financial Markets

From my list on cracking the trading code.

Why am I passionate about this?

I came from a left-brained family, with my father a bank Forex manager and my mother in the tax office before motherhood. I've always been mathematically minded and went into mechanical engineering before my second career in trading and finance. But saying this sustains the fallacy that you have to have a head for numbers to trade. That is nothing like the truth, and I hope my last book pick shows that I have learnt and come a long way from my initial beliefs. Trading is anything but mathematical, mechanistic, or even natural, you have to study and learn new ways of thinking and doing, and you can only succeed if you are open to this.

Alan's book list on cracking the trading code

Alan Northcott Why did Alan love this book?

This book has been the bible for technical analysts since its first iteration in 1985 and is a comprehensive guide to the established knowledge of the markets. It covers chart structure, trends, moving averages, oscillators, technical indicators, and all types of charts in the 542 pages of the 1999 edition, which added candlestick patterns to the older version, and is a great reference guide for all the traditional charting.

However, that is the latest edition, so it contains nothing on Ichimoku (cloud) charting, an incredibly interesting if esoteric development, which is one of the reasons I felt that I should write my book including these latest advances.

By John J. Murphy,

Why should I read it?

1 author picked Technical Analysis of the Financial Markets as one of their favorite books, and they share why you should read it.

What is this book about?

John J. Murphy has now updated his landmark bestseller Technical Analysis of the Futures Markets, to include all of the financial markets.

This outstanding reference has already taught thousands of traders the concepts of technical analysis and their application in the futures and stock markets. Covering the latest developments in computer technology, technical tools, and indicators, the second edition features new material on candlestick charting, intermarket relationships, stocks and stock rotation, plus state-of-the-art examples and figures. From how to read charts to understanding indicators and the crucial role technical analysis plays in investing, readers gain a thorough and accessible overview…


Book cover of Models of Society and Complex Systems

Charles H. Anderton Author Of Principles of Conflict Economics: The Political Economy of War, Terrorism, Genocide, and Peace

From my list on the economics of conflict and peace.

Why am I passionate about this?

Like many people, I am deeply troubled by the death and destruction from violent conflict. When I began my graduate work in economics at Cornell University, I was allowed to apply my economics learning to the problem of war. When I began teaching at Holy Cross College, my colleagues encouraged me to offer courses on the economics of war and peace. After many years of teaching, I compiled Principles of Conflict Economics (with John Carter) to serve as a textbook on economic aspects of conflict. I hope the book might encourage other economics professors and students to learn more about war and how to resolve conflicts nonviolently.

Charles' book list on the economics of conflict and peace

Charles H. Anderton Why did Charles love this book?

I appreciated how this book took on the challenge of applying advanced mathematical modeling and simulation techniques to gain new insights into the social evolution of norms and institutions in societies, which is a critical topic in many fields, including conflict and peace economics.

I learned much from the book’s coverage of selected conflict and peace topics such as riots, revolutions, the 2010 Arab Spring movement, and the social evolution of cooperation. I especially like how the mathematical models in the book are described intuitively using wonderfully imaginative diagrams.

In this way, both the mathematically and non-mathematically inclined can come away with a richer understanding of human behavior in dynamically changing social systems.

By Sebastian Ille,

Why should I read it?

1 author picked Models of Society and Complex Systems as one of their favorite books, and they share why you should read it.

What is this book about?

Models of Society and Complex Systems introduces readers to a variety of different mathematical tools used for modelling human behaviour and interactions, and the complex social dynamics that drive institutions, conflict, and coordination. What laws govern human affairs? How can we make sense of the complexity of societies and how do individual actions, characteristics, and beliefs interact? Social systems follow regularities which allow us to answer these questions using different mathematical approaches.

This book emphasises both theory and application. It systematically introduces mathematical approaches, such as evolutionary and spatial game theory, social network analysis, agent-based modelling, and chaos theory. It…


Book cover of Algorithmic and High-Frequency Trading

Ernest P. Chan Author Of Quantitative Trading: How to Build Your Own Algorithmic Trading Business

From my list on quantitative trading for beginners.

Why am I passionate about this?

A noted quantitative hedge fund manager and quant finance author, Ernie is the founder of QTS Capital Management and Predictnow.ai. Previously he has applied his expertise in machine learning at IBM T.J. Watson Research Center’s Human Language Technologies group, at Morgan Stanley’s Data Mining and Artificial Intelligence Group, and at Credit Suisse’s Horizon Trading Group. Ernie was quoted by Bloomberg, the Wall Street Journal, New York Times, Forbes, and the CIO magazine, and interviewed on CNBC’s Closing Bell program. He is an adjunct faculty at Northwestern University’s Master’s in Data Science program and supervises student theses there. Ernie holds a Ph.D. in theoretical physics from Cornell University.

Ernest's book list on quantitative trading for beginners

Ernest P. Chan Why did Ernest love this book?

Finally, for those who are not afraid of math, they should read this book because there is a lot of heavy-duty math. The good news for the rest of us is you can ignore all the math and still get a lot out of it, especially knowledge about market microstructure and how to find the theoretically optimal trading strategies given some assumptions about the price dynamics. Even if you don’t want to or can’t solve those darn stochastic differential equations, you can still implement a numerical approximation. At the minimum, you will learn common trading lingo such as “walking the book” or “the ITCH feed”.

By Alvaro Cartea, Sebastian Jaimungal, Jose Penalva

Why should I read it?

1 author picked Algorithmic and High-Frequency Trading as one of their favorite books, and they share why you should read it.

What is this book about?

The design of trading algorithms requires sophisticated mathematical models backed up by reliable data. In this textbook, the authors develop models for algorithmic trading in contexts such as executing large orders, market making, targeting VWAP and other schedules, trading pairs or collection of assets, and executing in dark pools. These models are grounded on how the exchanges work, whether the algorithm is trading with better informed traders (adverse selection), and the type of information available to market participants at both ultra-high and low frequency. Algorithmic and High-Frequency Trading is the first book that combines sophisticated mathematical modelling, empirical facts and…


Book cover of Credit Risk Modelling

Alain Ruttiens Author Of Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues

From my list on quantitative finance applied to financial markets.

Why am I passionate about this?

Having a master's degree in chemical engineering, I wasn't destined to work in the area of quantitative finance… the reason why I professionally moved to this discipline aren't worth exposing, but as a matter of fact, I've been quickly fascinated by this science, and encountered some of my favorites, such as maths and statistics, as used in the traditional activity of an engineer. And I had many opportunities of combining the knowledge and practice of financial markets with pragmatism, typically of the engineer’s education, i.e. oriented toward problem solving. In addition, I've always loved teaching, and writing books on financial markets & instruments, hence the importance I'm giving to pedagogy in professional books.

Alain's book list on quantitative finance applied to financial markets

Alain Ruttiens Why did Alain love this book?

In the vast array of quantitative finance relative to financial markets instruments and related risks, the case of credit or counterparty risk remains by far the most complex one, and thus, unsurprisingly, the least mastered by financial markets professionals.

A lot has been done, but a lot remains to be done: covering this is precisely the goal of this book. In a nutshell, the main obstacle to succeed in developing grounded and useful models of default prediction is due to the fact that a default is (fortunately) a rare event, in other words, with a (very) low probability of occurrence, and statistical tools are uncomfortable with very low probability levels. Hence the need of this book, to help the practitioner to go ahead in this matter.

By Terry Benzschawel,

Why should I read it?

1 author picked Credit Risk Modelling as one of their favorite books, and they share why you should read it.

What is this book about?

The book reveals to traders how to consistently outperform credit benchmarks, how to hedge the credit risk premium, and how to overcome pension liability deficits. In addition, several successful trading strategies are presented including debt versus equities, Co-Co bond trading and a quantitative analysis of the municipal bond market. Chapters include: Credit Models, Past Present and Future Predicting Annual Default Rates and Implications for Market Prices Risk and Relative Value in the Municipal Bond Market Contingent Collateral Bonds Model for Sovereign Default and Relative Value Beating Credit Benchmarks Analyzing and Hedging Systemic Liquidity Risk Building on the best-selling first edition,…


Book cover of The Complete Guide to Option Pricing Formulas

Alain Ruttiens Author Of Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues

From my list on quantitative finance applied to financial markets.

Why am I passionate about this?

Having a master's degree in chemical engineering, I wasn't destined to work in the area of quantitative finance… the reason why I professionally moved to this discipline aren't worth exposing, but as a matter of fact, I've been quickly fascinated by this science, and encountered some of my favorites, such as maths and statistics, as used in the traditional activity of an engineer. And I had many opportunities of combining the knowledge and practice of financial markets with pragmatism, typically of the engineer’s education, i.e. oriented toward problem solving. In addition, I've always loved teaching, and writing books on financial markets & instruments, hence the importance I'm giving to pedagogy in professional books.

Alain's book list on quantitative finance applied to financial markets

Alain Ruttiens Why did Alain love this book?

The valuation of options has been the subject of numerous studies, papers, and books.

The originality of this one is that it is collecting the resulting formulae to be used in practice, and for each of them, proposing related Excel spreadsheets, and VBA coding (also with a CD included). All types of options are covered, from “vanilla” to “exotics”, on every kind of underlyings (from traditional ones up to commodities and energy).

It also develops calculation methods for the options “greeks” and volatility. But the book is not only such a catalog of formulae, these are assorted by useful comments about the best way to apply them, and their validity limits. Not surprisingly, this book is qualified as the “bible” of options valuation.

By Espen Gaarder Haug,

Why should I read it?

1 author picked The Complete Guide to Option Pricing Formulas as one of their favorite books, and they share why you should read it.

What is this book about?

Long-established as a definitive resource by Wall Street professionals, The Complete Guide to Option Pricing Formulas has been revised and updated to reflect the realities of today's options markets. The Second Edition contains a complete listing of virtually every pricing formula_all presented in an easy-to-use dictionary format, with expert author commentary and ready-to-use programming code.

The Second Edition of this classic guide now includes more than 60 new option models and formulas...extensive tables providing an overview of all formulas...new examples and applications...and an updated CD containing all pricing formulas, with VBA code and ready-to-use Excel spreadsheets.

The volume also features…


Book cover of Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street

Barbara Rockefeller Author Of Technical Analysis For Dummies

From my list on for traders using technical analysis.

Why am I passionate about this?

Economics isn't really a good starting point for financial market analysis for the simple reason that its models are wildly inaccurate. As behaviorial economists like Daniel Kahneman have been showing, irrationality and the inability to measure risk properly are a very big component of the investment and trading decisions. But statistical risk management is also sloppy when applied to human behavior because people are not objects that reliably behave the same way under similar circumstances. So when you read an economist about markets or an engineer about risk management, you're missing a lot of the story. In the end, technical analysis is fascinating because how and why humans behave is an enduring mystery.

Barbara's book list on for traders using technical analysis

Barbara Rockefeller Why did Barbara love this book?

The subtitle is The Untold Story of the Scientific Betting System that Beat the Casinos and Wall Street. This book is an easy-to-read narrative of the intersection of the grimy underbelly of betting--with high-minded math. It reminds you that trading is not conducted in a clean little bubble. Technical analysis can give you an edge, but trading is still engaging in battle with opposing forces; strategy and tactics can count as much as building an elegant technical system. 

Your opponent on the trading battlefield will try to trick you, like a general in real warfare. He may keep selling and selling after you have bought, triggering a sell signal in your trading system. He is hunting for your sell signal. The mechanical response is to sell—your system says sell, and you should follow your system. To exit a position when the market goes against you is named a stop,…

By William Poundstone,

Why should I read it?

1 author picked Fortune's Formula as one of their favorite books, and they share why you should read it.

What is this book about?

In 1956, two Bell Labs scientists discovered the scientific formula for getting rich. One was mathematician Claude Shannon, neurotic father of our digital age, whose genius is ranked with Einstein's. The other was John L. Kelly Jr., a Texas-born, gun-toting physicist. Together they applied the science of information theory—the basis of computers and the Internet—to the problem of making as much money as possible, as fast as possible.

Shannon and MIT mathematician Edward O. Thorp took the "Kelly formula" to Las Vegas. It worked. They realized that there was even more money to be made in the stock market. Thorp…


Book cover of Option Trading: Pricing and Volatility Strategies and Techniques

Ernest P. Chan Author Of Quantitative Trading: How to Build Your Own Algorithmic Trading Business

From my list on quantitative trading for beginners.

Why am I passionate about this?

A noted quantitative hedge fund manager and quant finance author, Ernie is the founder of QTS Capital Management and Predictnow.ai. Previously he has applied his expertise in machine learning at IBM T.J. Watson Research Center’s Human Language Technologies group, at Morgan Stanley’s Data Mining and Artificial Intelligence Group, and at Credit Suisse’s Horizon Trading Group. Ernie was quoted by Bloomberg, the Wall Street Journal, New York Times, Forbes, and the CIO magazine, and interviewed on CNBC’s Closing Bell program. He is an adjunct faculty at Northwestern University’s Master’s in Data Science program and supervises student theses there. Ernie holds a Ph.D. in theoretical physics from Cornell University.

Ernest's book list on quantitative trading for beginners

Ernest P. Chan Why did Ernest love this book?

Disclaimer: I like Euan’s books not because he is a friend and has endorsed my books. Long before we became friends, I have bought his book, and said to myself “Wow! This is the first book about options trading that is not just a bunch of trite statements about payouts from various straddles and spreads positions!” It talks about some unique arbitrage opportunities that only professionals knew about. On the other hand, the amount of mathematics is very manageable, and can largely be skipped without affecting the practical applications of the concepts. 

By Euan Sinclair,

Why should I read it?

1 author picked Option Trading as one of their favorite books, and they share why you should read it.

What is this book about?

An A to Z options trading guide for the new millennium and the new economy Written by professional trader and quantitative analyst Euan Sinclair, Option Trading is a comprehensive guide to this discipline covering everything from historical background, contract types, and market structure to volatility measurement, forecasting, and hedging techniques. This comprehensive guide presents the detail and practical information that professional option traders need, whether they're using options to hedge, manage money, arbitrage, or engage in structured finance deals. It contains information essential to anyone in this field, including option pricing and price forecasting, the Greeks, implied volatility, volatility measurement…


Book cover of Algorithms to Live By: The Computer Science of Human Decisions

Michael L. Littman Author Of Code to Joy: Why Everyone Should Learn a Little Programming

From my list on computing and why it’s important and interesting.

Why am I passionate about this?

Saying just the right words in just the right way can cause a box of electronics to behave however you want it to behave… that’s an idea that has captivated me ever since I first played around with a computer at Radio Shack back in 1979. I’m always on the lookout for compelling ways to convey the topic to people who are open-minded, but maybe turned off by things that are overly technical. I teach computer science and study artificial intelligence as a way of expanding what we can get computers to do on our behalf.

Michael's book list on computing and why it’s important and interesting

Michael L. Littman Why did Michael love this book?

I always find myself applying algorithmic thinking in my everyday life—it affects the way I put away dishes, navigate to the store, and organize my to-do lists. And I think others could benefit from that mindset.

So, when I read this book, my reaction was "Yes! That's what I want people to know. I just wish I could have said it that well!" The authors (who I know, but didn't know they wrote a book together), did a fantastic job of selecting algorithms with deep human connections. Really! And they explain them just right, without getting too mathematical but while still hitting the key ideas with clarity and accuracy. Fantastic!

By Brian Christian, Tom Griffiths,

Why should I read it?

5 authors picked Algorithms to Live By as one of their favorite books, and they share why you should read it.

What is this book about?

A fascinating exploration of how computer algorithms can be applied to our everyday lives.

In this dazzlingly interdisciplinary work, acclaimed author Brian Christian and cognitive scientist Tom Griffiths show us how the simple, precise algorithms used by computers can also untangle very human questions. Modern life is constrained by limited space and time, limits that give rise to a particular set of problems. What should we do, or leave undone, in a day or a lifetime? How much messiness should we accept? The authors explain how to have better hunches and when to leave things to chance, how to deal…


Book cover of Consumption Takes Time: Implications for Economic Theory

Monica L. Smith Author Of Cities: The First 6,000 Years

From my list on why humans have so much stuff.

Why am I passionate about this?

I’m an archaeologist, which means that I’ve been lucky enough to travel to many places to dig and survey ancient remains. What I’ve realized in handling those dusty old objects is that all over the world, in both past and present, people are defined by their stuff: what they made, used, broke, and threw away. Most compelling are the things that people cherished despite being worn or flawed, just like we have objects in our house that are broken or old but that we keep anyway.

Monica's book list on why humans have so much stuff

Monica L. Smith Why did Monica love this book?

This looks like it’s the sternest and most boring book ever, but I love Steedman’s cool-and-collected ability to address the implications of the obvious: You can only do one thing at a time. You only have two hands. And when you’re with one set of belongings, you’re neglecting all the other stuff you own.

By Ian Steedman,

Why should I read it?

1 author picked Consumption Takes Time as one of their favorite books, and they share why you should read it.

What is this book about?

Standard economic theory of consumer behaviour considers consumers' preferences, their incomes and commodity prices to be the determinants of consumption. However, consumption takes time and no consumer has more - or less - than 168 hours per week. This simple fact is almost invisible in standard theory, and takes the centre stage in this book.