The Mathematics of Arbitrage / by Freddy Delbaen, Walter Schachermayer.

Springer eBooks

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).

This long-awaited book aims at 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 analyse the topic in the general framework of semi-martingale theory.

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