The Mathematics of Arbitrage [Paperback]

Proof of the Fundamental Theorem of Asset Pricing in its general form by Delbaen and Schachermayer was a milestone in the history of modern mathematical finance and now forms the cornerstone of this book.

Puts into book format a series of major results due mostly to the authors of this book.

Embeds highest-level research results into a treatment amenable to graduate students, with introductory, explanatory background.

Awaited in the quantitative finance community.

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, ală9