Probability Theory in Finance: A Mathematical Guide to the Black-Scholes Formula (Graduate Studies in Mathematics, Vol. 70) by Seán Dineen (PDF)

Description

The use of the Black-Scholes model and formula is pervasive in financial markets. There are very few undergraduate textbooks available on the subject and, until now, almost none written by mathematicians. Based on a course given by the author, the goal of this book is to introduce advanced undergraduates and beginning graduate students studying the mathematics of finance to the Black-Scholes formula. The author uses a first-principles approach, developing only the minimum background necessary to justify mathematical concepts and placing mathematical developments in context. The book skillfully draws the reader toward the art of thinking mathematically and then proceeds to lay the foundations in analysis and probability theory underlying modern financial mathematics. It rigorously reveals the mathematical secrets of topics such as abstract measure theory, conditional expectations, martingales, Wiener processes, the Itô calculus, and other ingredients of the Black-Scholes formula. In explaining these topics, the author uses examples drawn from the universe of finance. The book also contains many exercises, some included to clarify simple points of exposition, others to introduce new ideas and techniques, and a few containing relatively deep mathematical results. With the modest prerequisite of a first course in calculus, the book is suitable for undergraduates and graduate students in mathematics, finance, and economics and can be read, using appropriate selections, at a number of levels.

User’s Reviews

Editorial Reviews: Review “For budding financial engineers, this is an outstanding introduction to the mathematics that underlies derivatives pricing theory….It also offers plenty of exercises that will help you build mastery. “Dineen won an award (Best Books of 2006) for providing a treatment of finanical engineering math that is simultaneously accessible and rigorous.” —- Glyn Holton, founder Contingency Analysis and Riskbook.com”…an excellent choice … This book provides a thorough presentation of the mathematics behind the derivatives pricing formula. It is written for mathematicians as well as finance students or professionals.” —- MAA Reviews”…one of the author’s aims is to entice the students by the beauty of mathematics, which he illustrates very well. If a course instructor teaching from the book succeeds in this, my guess is that the course will be a great success. “It outshines most of its competitors … variety of nice exercises and solutions …” —- Mathematical Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is so unique in it’s approach. Most books are littered with equations and jargon, at the cost of a practical understanding of what we’re doing. So who cares if I’m using Lagrange Multipliers if I can’t explain it to the layman – that is the litmus test. This book uses such an approach, and balances practicality/common sense with equation solving.Pg 6 for example – simple problem of determining the Amount of annuity “similar practical checks will ensure….alert us to patently false conclusions”. In most books – “here is the equation, now go solve it” Not here – it’s the first time I’ve come across a book that recommends using your head. It’s as if the author is actually talking to you. I wish I had the chance of learning from Sean Dineen – I’m happy that I have his book to read atleast. His love for the subject is clear – in footnotes he mentions anecdotes (eg the detailed footnote on pg 8 on Euler and his contributions to the subject) and interesting facts that make the reading very entertaining. Prof Dineen – thank you so much for writing this book. My heart felt thanks!

⭐Advanced topic, but you still can make sense of most of the book’s chapters.

⭐well written book for entry level graduate courses, especially for those people with little math background. The delivery was insanely slow, but I bought this book at cheapest price that I can find, so I am ok with that.

⭐Amazing book. .learn everything you need to before starting rigorous quant studies. ..beautifully written book.

⭐Very satisfied

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