The Mathematics of Arbitrage

This book presents a rigorous mathematical treatment of the theory of pricing and hedging of derivative securities by the principle of "no arbitrage". The first part presents a relatively elementary introduction, restricting itself to the case of finite probability spaces. The second part consists of an updated edition of seven original research papers by the authors, which analyzes the topic in the general framework of semi-martingale theory.

The fundamental theorem of Asset Pricing due to 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 2 authors of this book Embeds highest-level research results into a treatment amenable to graduate students, with introductory, explanatory background Long-awaited in the quantitative finance community Includes supplementary material: sn.pub/extras

Autorentext

Walter Schachermeyer, born in 1950 in Linz, Austria, has received--as the first mathematician--the 1998 Wittgenstein Award, Austria's highest honor for scienctific achievement. Since 1998 he holds the Chair for Actuarial and Financial Mathematics at the Vienna University of Technolgoy. Among his achievements is the proof of the "Fundamental Theorem of Asset Pricing" in its general form, which was done in joint work with Freddy Delbaen. Freddy Delbaen, born in 1946 in Duffel/Antwerpen, Belgium, is Professor for Financial Mathematics at the ETH in Zurich since 1995.

Inhalt
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 Numéraire (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).