Description of Arbitrage Theory in Continuous Time
The second 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 measure theory, probability theory, Girsanov transformations, LIBOR and swap market models, and martingale representations, providing two full treatments of arbitrage pricing: the classical delta-hedging and the modern martingales. More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.
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 (For advanced readers)
11. The Mathematics of the Martingale Approach (For advanced readers)
12. Black-Scholes from a Martingale Point of View (For advanced readers)
13. Multidimensional Models: Classical Approach
14. Multidimensional Approach: Martingale Approach (For advanced readers)
15. Incomplete Markets
16. Dividends
17. Currency Derivatives
18. Barrier Options
19. Stochastic Optimal Control
20. Bonds and Interest Rates
21. Short Rate Models
22. Martingale Models for the Short Rate
23. Forward Rate Models
24. Change of Numeraire (For advanced readers)
25. LIBOR and Swap Market Models
26. Forwards and Futures
Appendix A Measure and Integration (For advanced readers)
Appendix B Probability Theory (For advanced readers)
Appendix C Martingales and Stopping Times (For advanced readers)
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