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Financial Mathematics: A Comprehensive Treatment (Textbooks in Mathematics)
Download Financial Mathematics: A Comprehensive Treatment (Textbooks in Mathematics)
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Review
"… brings together under a single cover a comprehensive and descriptive presentation of quantitative finance deftly organized into four major sections … A critically important acquisition for an academic library … especially recommended textbook for undergraduate and graduate students in the fields of mathematics, finance, actuarial science, and economics."―Library Bookwatch, April 2014 "As the owner of literally thousands of books on the mathematics of arbitrage, I’m sorely tempted to sell my collection and buy this book as a replacement. Or better yet, one for the office and one for the home office. I commend the authors for their authoritative and comprehensive treatment."―Peter Carr, PhD, Managing Director, Morgan Stanley, and Executive Director, NYU Courant Master of Science Program in Mathematics in Finance "This is a monumental effort to bring together topics from quantitative finance into one book; one no longer needs to go to different references to get the full scope of contents in the book. The authors treat the subjects rigorously but with plenty of examples, paying close attention to an audience that may encounter the subject matter for the first time, but aware that others will have seen it in different form earlier and may be looking for a different angle. This is a book that will find its way into classrooms worldwide."―Luis Seco, Professor, Department of Mathematics, University of Toronto
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Product details
Series: Textbooks in Mathematics
Hardcover: 829 pages
Publisher: Chapman and Hall/CRC; 1 edition (March 12, 2014)
Language: English
ISBN-10: 1439892423
ISBN-13: 978-1439892428
Product Dimensions:
7 x 1.8 x 10 inches
Shipping Weight: 3.4 pounds (View shipping rates and policies)
Average Customer Review:
4.2 out of 5 stars
7 customer reviews
Amazon Best Sellers Rank:
#1,370,389 in Books (See Top 100 in Books)
I was lucky enough to use this textbook in multiple classes. This is not only a huge benefit for students looking to save on books - but the cohesive nature of the text & notation connects concepts from various courses (probability theory; stochastic calculus; financial math) quite easily. For example, you may not get the same experience if you learned stochastic calculus and financial mathematics from two different textbooks.The authors did a great job covering pricing from various user levels (discrete; continuous; single asset; multi asset; path-dependent; etc) as well as all the math behind it (it -really- is quite comprehensive.) The problem sets are challenging enough to engage students/users but I found that the the sections that preceded the questions outlined clear (& often multiple) methods on solving similar problems. I would highly recommend this book to anyone with interest in quantitative finance, whether academically or professionally.
Bought this book early in my degree to use for 2 courses in financial math. I am just finishing up a course in Intro to Stochastic Calculus and this book was very very useful. I've tried to read through other books on Stochastic Calculus and they just seem to lack worked examples, proofs, and practice problems (mostly because I think the course is usually taught at a graduate level typically). But the authors clearly saw an opportunity and created a great book. I look forward to using it in future courses.And a note for future students: this is not an easy topic and requires a lot of work. I read and re-read sections as I make my own notes directly from the text. You cannot give a bad review if you've simply read sections once over quickly and don't practice the content
This is a very thorough and precise compendium of 99.99% of the mathematics used in the field of mathematical finance at the undergraduate and graduate level. At over 800 pages, you can consider this a mathematical finance bible of sorts! With the utmost rigour, Campolieti demonstrates his specialized knowledge in the field of Mathematical Finance—having earned his PhD in 1989 and taught Mathematical Finance for over two decades, Campolieti draws on his deep well of knowledge and experience to present otherwise obscure and technical results in an easy to digest manner. The authors use their mathematical prowess to bring a fresh and innovative approach to the concepts of Mathematical Finance—bringing mathematical rigour and intuition into his explanations and proofs.Do not listen to reviews that complain about the absence of a Student Solution Manual. Indeed, the problem sets are difficult. However, I have been informed that the authors are in the process of making the solutions manual available to the public. In many ways, the solutions manual will blow you away even more than the textbook, as the solutions are treated with extreme care and precision—providing you with explicit and step-by-step guides to the illuminating questions provided.This is a must-have for anyone who is serious about studying mathematical finance.
Firstly, I was an undergraduate student taught by these two professors so I bought this as a reference book to replace my class notes.Do note that I have not read everything from this book as this book is (much) bigger than Shreve's.-> Audience:This book is mainly for those pursuing the financial mathematics industry (as a student or as someone switching into the field). Financial mathematics mainly deals with options pricing and financial risk management.-> Mathematics Background & Chapters:For this book in particular the more mathematics,statistics (and maybe programming) one knows the better it is for self-study. Knowing real analysis can definitely help as some of the later chapters mention Borel sets, measure, Radon-Nikodym Derviative, etc.The first chapter deals with Time Value of Money, Annuities and Bonds and the second chapter is an introduction to pricing financial securities and some topics in portfolio theory. These first two chapters assume a background in calculus, a introductory probability and statistics and intro linear algebra.The later chapters assume the reader has knowledge in probability theory and there is a self-contained section on Stochastic Calculus which is the foundation for options pricing and risk management. Chapters also include the Binomial Asset Pricing Model (like in Shreve's Vol. 1) and Continuous Time Pricing Models (like in Shreve Vol. II). After the pricing models, there are sections dealing with Interest Rate models, Black-Scholes theory, options pricing, Change of Measure. The background assumed is probability theory, some real analysis and PDEs.There is one chapter which I think is a bit difficult. The chapter deals with the "Essentials of Probability Theory" which involves probability theory, real analysis, Borel sets and some Lebesgue integration ideas. This section is probably more suited for the financial mathematics researcher.In the last section of the book, there is a self-contained section on Monte Carlo Methods and Numerical methods for pricing and hedging financial securities. This section is nice for those interested in applying the theory (from earlier chapters) to practice.-> Book Formatting:I think the authors do a good job with having a section for list of notations with their meanings, a list of examples used, and some expectation indentities. There are no answers in the back of the book but the detailed and worked out examples are pretty good in the sense that they provide ideas and perspectives on solving questions and proofs.Similar to Shreve's Stochastic Calculus for Finance book, some proofs are omitted since they require some higher level mathematics.The self-contained Stochastic Calculus section was well done in my opinion. It was more detailed the Shreve's Vol II book. The examples in using Ito's Formula and solving SDEs was helpful.This book covered at least two or three courses in my Financial Mathematics undergrad under these guys. The value you get from this book is pretty darn good. I give this a book a 5 since it is a good reference and from my onw bias too. (If I was not biased, I might have given a 4.)I thought I'd give this review to give those an idea what this book is about as I highly disagreed with the one other review.
I was assigned this book for several fourth year undergraduate level courses. The text contains an advanced treatment of the type of mathematics needs for options pricing, including stochastic calculus and brownian motion.Ultimately, I have yet to find another text that covers this breadth on the topic, with this level of complexity. The book is well-written and self-contained. For any upper division mathematics student, this would be an excellent choice for studying financial mathematics.
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