Introduction to the Mathematics of Finance

Completely rewritten for its second edition, this book concentrates on discrete derivative pricing models, culminating in a thorough derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model.

The Mathematics of Finance has been a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced undergraduate or beginning graduate students in mathematics, finance or economics. This book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model.This second edition is a complete rewrite of the first edition with significant changes to the topic organization, thus making the book flow much more smoothly. Several topics have been expanded such as the discussions of options, including the history of options, and pricing nonattainable alternatives. In this edition the material on probability has been condensed into fewer chapters, and the material on the capital asset pricing model has been removed.The mathematics is not watered down, but it is appropriate for the intended audience. Previous knowledge of measure theory is not needed and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a "need-to-know" basis. No background in finance is required, since the book contains a chapter on options.

New edition fully rewritten, re-organized, and slimmed down to make the book flow more smoothly Classroom-tested for the past five years since the first edition Includes additional material on options and pricing nonattainable alternatives Excludes material on the capital asset pricing model, and condenses the material on probability in order to make the book more accessible to its readers Contains necessary background in financial matters for readers with little experience in finance

Autorentext
Steven Roman is currently an Emeritus Professor of Mathematics at the University of California. He is a prolific Springer author; some of his books include Field Theory, Advanced Linear Algebra, Introduction to Coding and Information Theory, and most recently Fundamentals of Group Theory.

Inhalt
Preface.- Notation Key and Greek Alphabet.- 0 Introduction.- Part 1 Options and Arbitrage.- 1 Background on Options.- 2 An Aperitif on Arbitrage.- Part 2 Discrete-Time Pricing Models.- 3 Discrete Probability.- 4 Stochastic Processes, Filtrations and Martingales.- 5 Discrete-Time Pricing Models.- 6 The Binomial Model.- 7 Pricing Nonattainable Alternatives in an Incomplete Market.- 8 Optimal Stopping and American Options.- Part 3 the Black-Scholes Option Pricing Formula.- 9 Continuous Probability.- 10 The Black-Scholes Option Pricing Formula.- Appendix A: Convexity and the Separation Theorem.- Appendix B: Closed, Convex Cones.- Selected Solutions.- References.- Index.