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Includes bibliographical references and index.

In 1994 and 1998 F. Delbaen and W. Schachermayer published two breakthrough papers where they proved continuous-time versions of the Fundamental Theorem of Asset Pricing. This is one of the most remarkable achievements in modern Mathematical Finance which led to intensive investigations in many applications of the arbitrage theory on a mathematically rigorous basis of stochastic calculus. Mathematical Basis for Finance: Stochastic Calculus for Finance provides detailed knowledge of all necessary attributes in stochastic calculus that are required for applications of the theory of stochastic integration in Mathematical Finance, in particular, the arbitrage theory. The exposition follows the traditions of the Strasbourg school. This book covers the general theory of stochastic processes, local martingales and processes of bounded variation, the theory of stochastic integration, definition and properties of the stochastic exponential; a part of the theory of Lévy processes. Finally, the reader gets acquainted with some facts concerning stochastic differential equations.

""Front Cover ""; ""Stochastic Calculus for Quantitative Finance ""; ""Copyright ""; ""Contents ""; ""Preface ""; ""Basic Notation ""

""List of Statements """"Chapter 1: General Theory of Stochastic Processes ""; ""1.1. Stochastic Basis and Stochastic Processes ""

""1.2. Stopping Times """"1.3. Measurable, Progressively Measurable, Optional and Predictable Ï?-algebras ""; ""1.4. Predictable Stopping Times ""; ""1.5. Totally Inaccessible Stopping Times ""

""2.1. Elements of the Theory of Martingales """"2.2. Local Martingales ""; ""2.3. Increasing Processes and Processes with Finite Variation ""

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