Arbitrage Theory in Continuous Time

Hardcover | September 26, 2009

byTomas Bjork

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The third edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous arbitrage pricing of financial derivatives, including stochastic optimal control theory and Merton's fund separation theory, the book is designed for graduate students and combines necessary mathematical background with a solid economic focus.It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. In this substantially extended new edition Bjork has added separate and complete chapters on the martingale approach to optimal investment problems, optimal stopping theory with applications to American options, and positive interest models and their connection to potential theory and stochasticdiscount factors.More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.

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From the Publisher

The third edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous arbitrage pricing of financial derivatives, including stochastic optimal control theory an...

Tomas Bjork is Professor of Mathematical Finance at the Stockholm School of Economics. His background is in probability theory and he was formerly at the Mathematics Department of the Royal Institute of Technology in Stockholm. He is co-editor of Mathematical Finance and Associate Editor of Finance and Stochastics. He has published nu...
Format:HardcoverDimensions:512 pages, 9.21 × 6.14 × 0.01 inPublished:September 26, 2009Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:019957474X

ISBN - 13:9780199574742

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Table of Contents

1. Introduction2. The Binomial Model3. A More General One period Model4. Stochastic Integrals5. Differential Equations6. Portfolio Dynamics7. Arbitrage Pricing8. Completeness and Hedging9. Parity Relations and Delta Hedging10. The Martingale Approach to Arbitrage Theory11. The Mathematics of the Martingale Approach12. Black-Scholes from a Martingale Point of View13. Multidimensional Models: Classical Approach14. Multidimensional Models: Martingale Approach15. Incomplete Markets16. Dividends17. Currency Derivatives18. Barrier Options19. Stochastic Optimal Control20. The Martingale Approach to Optimal Investment21. Optimal Stopping Theory and American Options22. Bonds and Interest Rates23. Short Rate Models24. Martingale Models for the Short Rate25. Forward Rate Models26. Change of Numeraire27. LIBOR and Swap Market Models28. Potentials and Positive Interest29. Forwards and FuturesA. Measure and IntegrationB. Probability TheoryC. Martingales and Stopping Times

Editorial Reviews

Review from previous edition: "This book is one of the best of a large number of new books on mathematical and probabilistic models in finance, positioned between the books by Hull and Duffie on a mathematical scale...This is a highly reasonable book and strikes a balance between mathematicaldevelopment and intuitive explanation" --Short Book Reviews