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 stochastic discount factors. More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.
Tomas Bjoerk 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 numerous journal articles on mathematical finance in general, and in particular on interest rate theory.
1. Introduction ; 2. The Binomial Model ; 3. A More General One period Model ; 4. Stochastic Integrals ; 5. Differential Equations ; 6. Portfolio Dynamics ; 7. Arbitrage Pricing ; 8. Completeness and Hedging ; 9. Parity Relations and Delta Hedging ; 10. The Martingale Approach to Arbitrage Theory ; 11. The Mathematics of the Martingale Approach ; 12. Black-Scholes from a Martingale Point of View ; 13. Multidimensional Models: Classical Approach ; 14. Multidimensional Models: Martingale Approach ; 15. Incomplete Markets ; 16. Dividends ; 17. Currency Derivatives ; 18. Barrier Options ; 19. Stochastic Optimal Control ; 20. The Martingale Approach to Optimal Investment ; 21. Optimal Stopping Theory and American Options ; 22. Bonds and Interest Rates ; 23. Short Rate Models ; 24. Martingale Models for the Short Rate ; 25. Forward Rate Models ; 26. Change of Numeraire ; 27. LIBOR and Swap Market Models ; 28. Potentials and Positive Interest ; 29. Forwards and Futures ; A. Measure and Integration ; B. Probability Theory ; C. Martingales and Stopping Times