Mathematics of Financial Markets [Hardcover]

Robert James Elliott (Author), P. Ekkehard Kopp (Author)

Book Description

Publication Date: December 21, 1998 | ISBN-10: 0387985530 | ISBN-13: 978-0387985534

The past five years have seen a number of introductory texts which focus on the applications of modern stochastic calculus to the theory of finance, and on the pricing models for derivative securities in particular. Some of these books develop the mathematics very quickly, making substantial demands on the reader's background in advanced probability theory. Others emphasize the financial applications and do not attempt a rigorous coverage of the continuous-time calculus. This book provides a rigorous introduction for those who do not have a good background in stochastic calculus. The emphasis is on keeping the discussion self-contained rather than giving the most general results possible.

Editorial Reviews

Review

From the reviews: "...This book is a valuable addition to a graduate student's reference collection. The number of textbooks in mathematical finance is increasing much faster than the number of revolutionary contributions to the field, but this text stands above the crowd." SIAM Review, December 2005 From the reviews of the second edition: "The book is very carefully formatted. … this book is a valuable addition to a graduate student’s reference collection. The number of textbooks in mathematical finance is increasing much faster than the number of revolutionary contributions to the field, but this text stands above the crowd." (Alexandre D’Aspremont, SIAM Reviews, December, 2005) "The emphasis of the first edition of this book was on developing the mathematical concepts for the rapidly expanding field of mathematical finance. This second edition contains a significant number of changes and additions … . The target audience is readers with sound mathematical background on elementary concepts from measure-theoretic probability … . It should be an equally valuable resource to practitioners interested in the mathematical tools … . will be a very useful addition to any scholarly library." (Theofanis Sapatinas, Journal of Applied Sciences, Vol. 32 (6), 2005) "The second edition adds new matieral from current active research areas. A new chapter on coherent risk measures for instance reflects the recent trend in research and applications in the area of risk management. In summary, this is an excellent textbook in mathematical finance, and I can definitely recommend it." (S. Peng, Short Book Reviews of the ISI, June 2006) --This text refers to an alternate Hardcover edition.

From the Back Cover

This book presents the mathematics that underpins pricing models for derivative securities, such as options, futures and swaps, in modern financial markets. The idealized continuous-time models built upon the famous Black-Scholes theory require sophisticated mathematical tools drawn from modern stochastic calculus. However, many of the underlying ideas can be explained more simply within a discrete-time framework. This is developed extensively in this substantially revised second edition to motivate the technically more demanding continuous-time theory, which includes a detailed analysis of the Black-Scholes model and its generalizations, American put options, term structure models and consumption-investment problems. The mathematics of martingales and stochastic calculus is developed where it is needed. The new edition adds substantial material from current areas of active research, notably: a new chapter on coherent risk measures, with applications to hedging a complete proof of the first fundamental theorem of asset pricing for general discrete market models the arbitrage interval for incomplete discrete-time markets characterization of complete discrete-time markets, using extended models risk and return and sensitivity analysis for the Black-Scholes model The treatment remains careful and detailed rather than comprehensive, with a clear focus on options. From here the reader can progress to the current research literature and the use of similar methods for more exotic financial instruments. The text should prove useful to graduates with a sound mathematical background, ideally a knowledge of elementary concepts from measure-theoretic probability, who wish to understand the mathematical models on which the bewildering multitude of current financial instruments used in derivative markets and credit institutions is based. The first edition has been used successfully in a wide range of Master’s programs in mathematical finance and this new edition should prove even more popular in this expanding market. It should equally be useful to risk managers and practitioners looking to master the mathematical tools needed for modern pricing and hedging techniques. Robert J. Elliott is RBC Financial Group Professor of Finance at the Haskayne School of Business at the University of Calgary, having held positions in mathematics at the University of Alberta, Hull, Oxford, Warwick, and Northwestern. He is the author of over 300 research papers and several books, including Stochastic Calculus and Applications, Hidden Markov Models (with Lahkdar Aggoun and John Moore) and, with Lakhdar Aggoun, Measure Theory and Filtering: Theory and Applications. He is an Associate Editor of Mathematical Finance, Stochastics and Stochastics Reports, Stochastic Analysis and Applications and the Canadian Applied Mathematics Quarterly. P. Ekkehard Kopp is Professor of Mathematics, and a former Pro-Vice-Chancellor, at the University of Hull. He is the author of Martingales and Stochastic Integrals, Analysis and, with Marek Capinski, of Measure, Integral and Probability. He is a member of the Editorial Board of Springer Finance.   --This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 304 pages
• Publisher: Springer Verlag (December 21, 1998)
• Language: English
• ISBN-10: 0387985530
• ISBN-13: 978-0387985534
• Product Dimensions: 9.5 x 6.3 x 0.7 inches
• Shipping Weight: 1.3 pounds
• Average Customer Review: 4.5 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #1,803,263 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

4.0 out of 5 stars Be careful of typos!, September 11, 2009

By 

B. Hertz Shargel - See all my reviews
(REAL NAME)   

This review is from: Mathematics of Financial Markets (Springer Finance) (Hardcover)

This book provides a speedy but readable and comprehensive approach to financial math. For a slower and more careful approach to the mathematics, especially with regard to local martingales and the construction of the stochastic integral, I recommend Steele. An important warning about the 2nd edition of Elliott and Kopp is that Chapter 7, the longest and most important chapter in the book, which covers continuous time European options and the Greeks, is *rife* with typos: incorrect subscripts, superscripts and signs, mixed up or missing variables in expressions, backwards inequalities, etc. This chapter was clearly not edited carefully, and can be a little frustrating to read.

4.0 out of 5 stars A Good book for Martingale approach, July 6, 2000

By 

Vincent Chan (Hong Kong,China) - See all my reviews

This review is from: Mathematics of Financial Markets (Hardcover)

This book discusses the financial mathematics from the view of martingale approaches. It is good for someone who want to price derivatives by martingale approach. Unfortunately, this book lacks talking about exotic options like average options,lookback options and passport options.

5 of 9 people found the following review helpful:

5.0 out of 5 stars Excellent - Good Mathematical Level, May 3, 2001

By 

Alberto Dominguez - See all my reviews
(VINE VOICE)    (REAL NAME)   

This review is from: Mathematics of Financial Markets (Hardcover)

Does an excellent job of presenting the mathematics WITH RIGOR. The mathematics is more mature than Bingham & Kiesel, but the book is more accessible and far more readable than the similar texts by Karatzas & Shreve and Musiela & Rutkowski.