Arbitrage Theory in Continuous Time

Front Cover
Oxford University Press, 1998 - Arbitrage - 312 pages
Professor Bjork provides an accessible introduction to the classical underpinnings of the central mathematical theory behind modern finance. Combining sound mathematical principles with the necessary economic focus, Arbitrage Theory in Continuous Time is specifically designed for graduate students, and includes solved examples for every new technique presented, numerous exercises, and Further Reading lists for each chapter. -;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 Bj--ouml--;rk 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 marketmodels. 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 selfcontained 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.
 

Contents

1 Introduction
1
2 The Binomial Model
6
3 Stochastic Integrals
27
4 Differential Equations
52
5 Portfolio Dynamics
69
6 Arbitrage Pricing
76
7 Completeness and Hedging
99
8 Parity Relations and Delta Hedging
108
13 Barrier Options
182
14 Stochastic Optimal Control
198
15 Bonds and Interest Rates
228
16 Short Rate Models
242
17 Martingale Models for the Short Rate
252
18 Forward Rate Models
266
19 Change of Numeraire
274
20 Forwards and Futures
297

9 Several Underlying Assets
119
10 Incomplete Markets
135
11 Dividends
154
12 Currency Derivatives
167

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