本书是Springer《数学研究生丛书》之113卷,是国内外公认的金融数学经典教材,各章有习题详解。本书初版于1988年,1991年出第2版,之后Springer已重印8次,本书是2005年的第8次重印版。

Preface
Suggestions for the Reader
Interdependence of the Chapters
Frequently Used Notation
CHAPTER 1 Martingales, Stopping Times, and Filtrations
1.1. Stochastic Processes and (y-Fields
1.2. Stopping Times
1.3. Continuous-Time Martingales
1.4. The Doob-Meyer Decomposition
1.5. Continuous, Square-Integrable Martingales
1.6. Solutions to Selected Problems
1.7. Notes
CHAPTER 2 Brownian Motion
2.1. Introduction
2.2. First Construction of Brownian Motion
2.3. Second Construction of Brownian Motion
2.4. The Space C[0, ∞), Weak Convergence, and Wiener Measure
2.5. The Markov Property
2.6. The Strong Markov Property and the Reflection Principle
2.7. Brownian Filtrations
2.8. Computations Based on Passage Times
2.9. The Brownian Sample Paths
2.10. Solutions to Selected Problems
2.11. Notes
CHAPTER 3 Stochastic Integration
3.1 Introduction
3.2 Construction of the Stochastic Integral
3.3 The Change-of-Variable Formula
3.4 Representations of Continuous Martingales in Terms of Brownian Motion
……
CHAPTER 4 Brownian Motion and Partial Differential Equations
CHAPTER 5 Stochastic Differential Equations
CHAPTER 6 P.Levy's Theory of Brownian Local Time
Bibliography
Index