自三十多年前Black和Scholes的开创性工作出现以来，金融数学这个现代学科无论在理论还是实践方面都经历了巨大发展。《金融数学引论（英文版）》旨在介绍部分基础理论，使得学生和研究人员了解后能够阅读更高级的教科书和研究文章。
《金融数学引论（英文版）》一开始讨论了欧式和美式衍生产品在离散二叉树模型（即离散时间和离散状态）下套期保值和定价的基本思想的发展，然后介绍了一个一般的离散有限市场模型，并在此场合中证明了资产定价的一些基本定理。概率论中的诸如条件期望、滤波、（超）鞅、等价鞅测度、鞅表示等工具，在这个简单的离散框架下被首次用到，从而搭建了通向连续（时间和状态）场合的桥梁，后者需要布朗运动和随机分析的概念。连续场合中*简单的模型是著名的Black-Scholes模型，欧式和美式衍生产品的定价和套期保值因此有所发展。《金融数学引论（英文版）》*后介绍了连续市场模型的一些基本定理，这个模型在多个方面推广了简单Black-Scholes模型。
Preface
Chapter 1．Financial Markets and Derivatives
1．1．Financial Markets
1．2．Derivatives
1．3．Exercise
Chapter 2．Binomial Model
2．1．Binomial or CRR Model
2．2．Pricing a European Contingent Claim
2．3．Pricing an American Contingent Claim
2．4．Exercises
Chapter 3．Finite Market Model
3．1．Definition of the Finite Market Model
3．2．First Fundamental Theorem of Asset Pricing
3．3．Second Fundamental Theorem of Asset Pricing
3．4．Pricing European Contingent Claims
3．5．Incomplete Markets
3．6．Separating Hyperplane Theorem
3．7．Exercises
Chapter 4．Black-Scholes Model
4．1．Preliminaries
4．2．Black-Scholes Model
4．3．Equivalent Martingale Measure
4．4．European Contingent Claims
4．5．Pricing European Contingent Claims
4．6．European Call Option - Black-Scholes Formula
4．7．American Contingent Claims
4．8．American Call Option
4．9．American Put Option
4．10．Exercises
Chapter 5．Multi-dimensional Black-Scholes Model
5．1．Preliminaries
5．2．Multi-dimensional Black-Scholes Model
5．3．First Fundamental Theorem of Asset Pricing
5．4．Form of Equivalent Local Martingale Measures
5．5．Second Fundamental Theorem of Asset Pricing
5．6．Pricing European Contingent Claims
5．7．Incomplete Markets
5．8．Exercises
Appendix A．Conditional Expectation and LP-Spaces
Appendix B．Discrete Time Stochastic Processes
Appendix C．Continuous Time Stochastic Processes
Appendix D．Brownian Motion and Stochastic Integration
D．1．Brownian Motion
D．2．Stochastic Integrals (with respect to Brownian motion)
D．3．Ito Process
D．4．Ito Formula
D．5．Girsanov Transformation
D．6．Martingale Representation Theorem
Bibliography
Index
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