Arbitrage theory in continuous time

著者

書誌事項

Arbitrage theory in continuous time

Tomas Björk

Oxford University Press, 1998

大学図書館所蔵 件 / 全35件

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注記

Includes bibliography (p. [303]-307) and index

内容説明・目次

内容説明

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 Tomas Bjork has added completely new chapters on measure theory and probability theory, including the Radon-Nikodym Theorem, Girsanov transformations, and stochastic integral martingale representations. There is also an extensive new chapter on the abstract martingale approach to arbitrage theory, including a guided tour through the Delbaen-Schachermayer proof of the first fundamental theorem, as well as a new chapter on the LIBOR and swap market models. Providing two full treatments of arbitrage theory - the classical delta hedging approach and the modern martingale approach - the book is written in such a way that these approaches can be studied independently of each other, thus providing the less mathematically oriented reader with a self contained introduction to arbitrage theory, while at the same time allowing the specialist to see the full theory in action. This is the textbook of choice for graduate students and advanced undergraduates studying finance and an invaluable introduction to mathematical finance for mathematicians and professionals in financial markets.

目次

  • 1. Introduction
  • 2. The Binomial Model
  • 3. Stochastic Integrals
  • 4. Differential Equations
  • 5. Portfolio Dynamics
  • 6. Arbitrage Pricing
  • 7. Complete Markets
  • 8. Properties of the Pricing Formulae
  • 9. Several Underlying Assets
  • 10. Incomplete Markets
  • 11. Barrier Options
  • 12. Dividends
  • 13. Currency Derivatives
  • 14. Stochastic Optimal Control
  • 15. The Term Structure of Interest Rates
  • 16. Short Rate Models
  • 17. Forward Rate Models
  • 18. Change of Numeraire

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