Details
- New edition building on the strengths of a successful graduate text
- A clear, accessible introduction to a complex field of classical financial mathematics
- Includes solved examples for all techniques, exercises, and further reading.
New to this edition
- 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.
- Updated definition of arbitrage in Chapter 3 that has the advantage that martingale measures will be equivalent to the objective measure instead of merely absolutely continuous.
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.
Readership: Graduate students and advanced undergraduates studying finance. Mathematicians looking for an introduction to mathematical finance. Professionals in financial markets
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
Tomas Björk, Professor of Mathematical Finance, Stockholm School of Economics
Review(s) 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 mathematical development and intuitive explanation - Short Book Reviews
