Optimization Methods in Finance (Mathematics, Finance and Risk) [Hardcover]

Gerard Cornuejols (Author), Reha Tutuncu (Author)

Book Description

ISBN-10: 0521861705 | ISBN-13: 978-0521861700 | Publication Date: January 8, 2007

Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses.

Editorial Reviews

Review

"This book will be useful as a textbook for students in financial engineering at the MS level.... The book will also be of interest to researchers and graduate students in optimization who are interested in applications of optimization to financial problems."
Brian Borchers, Journal of Online Mathematics and its Applications

Book Description

Discusses optimization problems encountered in financial models, describes the relevant theory and efficient solution methods, and shows how to apply them to practical problems in mathematical finance. Based on a successful course at CMU, the text is class-tested and meets the need for a textbook aimed at financial applications.

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Product Details

• Hardcover: 358 pages
• Publisher: Cambridge University Press (January 8, 2007)
• Language: English
• ISBN-10: 0521861705
• ISBN-13: 978-0521861700
• Product Dimensions: 9.8 x 7.1 x 0.9 inches
• Shipping Weight: 1.7 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #130,262 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

7 of 9 people found the following review helpful:

5.0 out of 5 stars Modern view, balanced coverage of optimization methods for quantitative finance, March 29, 2007

By 

tahoedenizen "tahoedenizen" (Incline Village, NV United States) - See all my reviews

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This review is from: Optimization Methods in Finance (Mathematics, Finance and Risk) (Hardcover)

This is a very up-to-date book featuring complete, balanced coverage of optimization methods used in quantitative finance. It should be a great resource for practitioners in financial engineering or portfolio management who need to know what methods to apply to different problems, and how to evaluate competing vendor claims, without going too deeply into the algorithmic details of each optimization method.

The book has 20 chapters that alternate between an overview of a class of optimization methods, then a set of examples applying those methods to problems in quantitative finance:

* Linear programming, with applications to asset/liability cash flow matching and arbitrage detection

* Nonlinear programming, with applications to volatility estimation

* Quadratic programming, with good coverage of mean-variance portfolio optimization

* Conic optimization, with several applications: index tracking, approximating covariance matrices, recovering risk-neutral probabilities from option prices

* Integer programming, with applications to index fund construction and combinatorial auctions

* Dynamic programming, with applications to pricing American options

* Stochastic programming, with applications that minimize Conditional Value at Risk, and manage assets and liabilities over multiple periods

* Robust optimization, with models to deal with estimation risk in portfolio optimization

It's difficult to find another book with this breadth of coverage of optimization methods, especially with a focus on quantitative finance. It's also difficult to find another book that treats modern methods of conic optimization and robust optimization, which have growing importance in finance.

Granted, the treatment of the different applications is not meant to be comprehensive -- it's really just enough to give the reader an idea of how each problem can be approached, with appropriate references to the academic literature to learn more. There are some references to available software for the different methods, but this is a brief and partial snapshot; commercial software for the newer methods is getting better all the time.

Appendices provide brief, helpful introductions to four key technical topics in optimization: Convexity, cones, probability, and the revised Simplex method. An understanding of convexity and cones is essential to an appreciation of modern methods of conic and robust optimization, and certainly anyone working in this field needs an understanding of probability and the Simplex method for linear programming.

I believe this book fills a need that has existed for some time: For the quantitative finance practitioner with way too much technical literature to deal with, it provides a comprehensive, modern introduction to optimization methods that makes efficient use of the reader's time. It's well worth the price for someone working in this field.

2 of 2 people found the following review helpful:

3.0 out of 5 stars Great book - where are the worked examples??, September 2, 2011

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journeyman - See all my reviews

This review is from: Optimization Methods in Finance (Mathematics, Finance and Risk) (Hardcover)

I picked up this slightly pricey book because I wanted to teach myself OR as applied to finance. I deliberately selected this text because (a) Its partly based on the well-regarded Carnegie Mellon quant finance courses; and (b) there are few prerequisites that i can see to use this book.

While I find the book to be well-written and an excellent introduction to OR for even entry level students, what makes me disappointed is the fact that almost none of the examples in the book have worked solutions. Neither does there appear to be a separate solution manual (which I would be prepared to purchase) nor have the authors appeared to supply one on their websites.

Its a basic principle for learning mathematics that you need worked examples! You might argue that the solutions can be worked through with an instructor, but what about those of us using it on a standalone basis?

For these reasons i am knocking it down to only three stars. Show me a solution manual or provide them for download and will gladly bump it up to 5 stars!

3 of 4 people found the following review helpful:

5.0 out of 5 stars Wonderful book with lots of financial applications, August 22, 2007

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LOV - See all my reviews

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This review is from: Optimization Methods in Finance (Mathematics, Finance and Risk) (Hardcover)

This book is very well-written with some theories and tons of financial applications. I hadn't thought that a GARCH model for estimating stochastic volatility can be seen as a nonlinear programming application. It touches some relatively modern/advanced topics such as robust optimization and cone optimization. It's just a wonderful optimization book for financial engineers and people in the financial industry.