沃顿商学院 金融随机分析课程
1. Random walks and first step analysis
2. First martingale steps
3. Brownian motion
4. Martingales: The next steps
5. Richness of paths
6. Itô integration
7. Localization and Itô's integral
8. Itô's formula
9. Stochastic differential equations
10. Arbitrage and SDEs
11. The diffusion equation
12. Representation theorems
13. Girsanov theory
14. Arbitrage and martingales
15. The Feynman-Kac connection
Appendix I: Mathematical Tools
Appendix II: Comments and Credits

"... a book that is a marvelous first step for the person wanting a rigorous development of stochastic calculus, as well as its application to derivative pricing. By focusing solely on Brownian motion, the reader is able to develop an intuition and a feel for how to go about solving problems as well as deriving results." --- Mark A. Cassano (see the full review from the Journal of Finance)
"The main results are reinforced with simple special cases, and only when the intuitive foundations are laid does the author resort to the formalism of probability.... This is one of the most interesting and easiest reads in the discipline; a gem of a book." --- D. L. McLeish in Short Book Reviews
"...the results are presented carefully and thoroughly, and I expect that readers will find that this combination of a careful development of stochastic calculus with many details and examples is very useful and will enable them to apply the whole theory confidently." --- Martin Schweizer (Berlin) from the review in Zentralblatt fur Mathematik: (0962.60001) "I thoroughly enjoyed reading this book. The author is to be complimented for his efforts in providing many useful insights behind the various theories. It is a superb introduction to stochastic calculus and Brownian motion." --- Elias Shiu (from the review in JASA)