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A Linear Algebra Primer for Financial Engineering: Covariance Matrices, Eigenvectors, OLS, and more (Financial Engineering Advanced Background Series)

by Dan Stefanica (Author)
4.7 4.7 out of 5 stars 22 ratings
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This book covers linear algebra methods for financial engineering applications from a numerical point of view. The book contains many such applications, as well as pseudocodes, numerical examples, and questions often asked in interviews for quantitative positions.

Financial Applications

• The Arrow—Debreu one period market model

• One period index options arbitrage

• Covariance and correlation matrix estimation from time series data

• Ordinary least squares for implied volatility computation

• Minimum variance portfolios and maximum return portfolios

• Value at Risk and portfolio VaR

Linear Algebra Topics

• LU and Cholesky decompositions and linear solvers

• Optimal solvers for tridiagonal symmetric positive matrices

• Ordinary least squares and linear regression

• Linear Transformation Property

• Efficient cubic spline interpolation

• Multivariate normal random variables

The book is written in a similar spirit as the best selling ``A Primer for the Mathematics of Financial Engineering" by the same author, and should accordingly be useful to a similarly large audience:

• Prospective students for financial engineering or mathematical finance programs will be able to self-study material that will prove very important in their future studies

• Finance practitioners will find mathematical underpinnings for many methods used in practice, furthering the ability to expand upon these methods

• Academics teaching financial engineering courses will be able to use this book as textbook, or as reference book for numerical linear algebra methods with financial applications.

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  1. ISBN-10
    0979757657
  2. ISBN-13
    978-0979757655
  3. Publication date
    July 7, 2014
  4. Book 3 of 4
    Financial Engineering Advanced Background Series
  5. Language
    English
  6. Dimensions
    6 x 0.77 x 9 inches
  7. Print length
    340 pages
  8. See all details
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A Linear Algebra Primer for Financial Engineering: Covariance Matrices, Eigenvectors, OLS, and more (Financial Engineering Ad
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A Primer For The Mathematics Of Financial Engineering, Second Edition (Financial Engineering Advanced Background Series)
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Product details

  • Publisher ‏ : ‎ FE Press, LLC (July 7, 2014)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 340 pages
  • ISBN-10 ‏ : ‎ 0979757657
  • ISBN-13 ‏ : ‎ 978-0979757655
  • Item Weight ‏ : ‎ 1.28 pounds
  • Dimensions ‏ : ‎ 6 x 0.77 x 9 inches
  • Customer Reviews:
    4.7 4.7 out of 5 stars 22 ratings

About the author

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Dan Stefanica

Dan Stefanica

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Dan Stefanica has been the Director of the Financial Engineering MS Program at Baruch College, City University of New York, since its inception in 2002, and is the author of the best-selling ``A Primer For The Mathematics Of Financial Engineering" and ``A Linear Algebra Primer for Financial Engineering: Covariance Matrices, Eigenvectors, OLS, and more", and co-author of ``150 Most Frequently Asked Questions on Quant Interviews". He teaches graduate courses on numerical methods for financial engineering, as well as pre-program courses on advanced calculus and numerical linear algebra with financial applications. His research spans numerical analysis, graph theory, and geophysical fluid dynamics. He has a PhD in mathematics from New York University and taught previously at the Massachusetts Institute of Technology. Dan was a silver medalist at the International Mathematics Olympiad, and coached the MIT and NYU teams for the William Lowell Putnam math competition.

Customer reviews

4.7 out of 5 stars
4.7 out of 5
22 global ratings

Top reviews from the United States

NY customer
5.0 out of 5 stars A gem of a book - clear and with great examples
Reviewed in the United States on April 21, 2023
Verified Purchase
This is my favorite book for math finance knowledge. It was never fully clear to me how matrix decompositions work until reading this book. I implemented the code and the examples were very useful to make sure there were no bugs. The linear solvers for symmetric tridiagonal matrices were incredibly insightful and I implemented the method at work. Colleagues were very impressed.

You will understand the linear algebra behind least squares, Markowitz portfolio optimization, and other a lot better after reading this book. A gem!
One person found this helpful
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Amazon Customer
5.0 out of 5 stars Unarguably the best Linear Algebra primer out there for applications to finance
Reviewed in the United States on March 12, 2016
Verified Purchase
Unarguably the best Linear Algebra primer out there for applications to finance. Broad range of topics covered with great depth. I often use it as a quick reference guide.
5 people found this helpful
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Amazon Customer
5.0 out of 5 stars it is in good
Reviewed in the United States on September 24, 2016
Verified Purchase
thank you for the book. it is in good condition
4 people found this helpful
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dmq
5.0 out of 5 stars Five Stars
Reviewed in the United States on October 12, 2014
Verified Purchase
Excellent book!
3 people found this helpful
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Ijon Tichy
5.0 out of 5 stars Comprehensive survey of linear algebra for finance professionals
Reviewed in the United States on October 2, 2014
This book, modestly titled as a "linear algebra primer", is, in fact, a well written comprehensive introduction to the uses of linear algebra techniques in finance. The emphasis lies on concrete, computer software implementable linear algebra with a wide range of specific applications to portfolio construction, market data analysis, and derivatives pricing. It will be a valuable resource not only for its targeted audience, namely graduate students in financial engineering, but also, more broadly, for business professionals whose work relies of quantitative techniques.
15 people found this helpful
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frank
1.0 out of 5 stars One Star
Reviewed in the United States on April 15, 2018
Verified Purchase
I got the wrong book
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2 cents worth
4.0 out of 5 stars This book doesn't teach Linear Algebra but shows financial engineering applicatons of it.
Reviewed in the United States on August 8, 2014
This book is not A Linear Algebra Primer for Financial Engineering...
It is a Primer on Applying Basic Linear Algebra in Financial Engineering...
That is the book doesn't teach much Linear Algebra...what it does is show how to apply
linear algebra to Financial Engineering...but you have to know Linear Algebra ( at the college undergrad linear algebra level)
to make much use of the book. But if you are comfortable with Linear Algebra there are some useful applications.
24 people found this helpful
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Top reviews from other countries

AD
5.0 out of 5 stars Must have
Reviewed in France on March 28, 2019
Verified Purchase
Highly recommend!
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