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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…mehr

Produktbeschreibung
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.
  • Produktdetails
  • Undergraduate Texts in Mathematics
  • Verlag: Springer, Berlin
  • Artikelnr. des Verlages: 86072058
  • 2. Aufl.
  • Seitenzahl: 304
  • Erscheinungstermin: 24. April 2012
  • Englisch
  • Abmessung: 244mm x 161mm x 22mm
  • Gewicht: 590g
  • ISBN-13: 9781461435815
  • ISBN-10: 1461435811
  • Artikelnr.: 34985179
Autorenporträt
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.
Inhaltsangabe
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
Rezensionen
From the reviews of the first edition: "The book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formula as a limiting case of the Cox-Ross-Rubinstein discrete model. ... The mathematics is not watered down but is appropriate for the intended audience. ... No background in finance is required, since the book also contains a chapter on options." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 50 (3-4), 2004) "The book is basically a textbook on the mathematics of financial derivatives on equity ... . The text covers the material with precision, with detailed discussions, not avoiding the topics that require a bit more of mathematical maturity, and this it does with clarity. In particular, the discussion of optimal stopping is clear and detailed." (Eusebio Corbache, Zentralblatt MATH, Vol. 1068, 2005)