The Mathematics of Arbitrage [Hardcover]

A Guided Tour to Arbitrage Theory.- The Story in a Nutshell.- Models of Financial Markets on Finite Probability Spaces.- Utility Maximisation on Finite Probability Spaces.- Bachelier and Black-Scholes.- The Kreps-Yan Theorem.- The Dalang-Morton-Willinger Theorem.- A Primer in Stochastic Integration.- Arbitrage Theory in Continuous Time: an Overview.- The Original Papers.- A General Version of the Fundamental Theorem of Asset Pricing (1994).- A Simple Counter-Example to Several Problems in the Theory of Asset Pricing (1998).- The No-Arbitrage Property under a Change of Num?raire (1995).- The Existence of Absolutely Continuous Local Martingale Measures (1995).- The Banach Space of Workable Contingent Claims in Arbitrage Theory (1997).- The Fundamental Theorem of Asset Pricingfor Unbounded Stochastic Processes (1998).- A Compactness Principle for Bounded Sequences of Martingales with Applications (1999).

From the reviews:

As a learning device, I think this works really well. The second half of the book allows readers to put to use the mathematics they learn in the first half. I really like the authors writing style. They provide plenty of intuitive insights and historical notes along the way as they formally develop concepts. & I recommend it highly to theoretically-inclined financial engineers and researchers. (www.riskbook.com, September, 2006)

The aim of the book, as the authors state & is to give the reader a guided tour through the mathematics of arbitrage. & The book will be of invaluable help to new researchers in the area of incomplete markets. A new graduate student wishing to do such research would start by reading the papers in the book. She or he now has a very good book to assist this study. (Angelos Dassios, Mathematical Reviews, Issue 2007 a)

Walter Schachermeyer, born in 1950 in Linz, Austria, has received--as the first mathematician--the 1998 Wittgenstein Award, AuslÓ)