金融随机分析(第2卷)

　　这是一套随机分析在定量经济学领域中应用方面的著名教材，作者在该领域享有盛誉，全书共分2卷。第1卷主要包括随机分析的基础性知识和离散时间模型；第2卷主要包括连续时间模型和该模型经济学中的应用。就其内容而言，第2卷有较为实际的可操作性的定量经济学内容，同时也包含了较为完整的随机微分方程理论。本书各章有习题，适用于掌握微积积分基础知识的大学高年级本科生和硕士研究生。
　　

1 general probability theory
1.1 infinite probability spaces
　1.2 random variables and distributions
　1.3 expectations
　1.4 convergence of integrals
　1.5 computation of expectations
　1.6 change of measure
　1.7 summary
　1.8 notes
　1.9 exercises
2 information and conditioning
　2.1 information and or-algebras
　2.2 independence
　2.3 general conditional expectations
　2.4 summary
　2.5 notes
　2.6 exercises
3 brownian motion
　3.1 introduction
　3.2 scaled random walks

　　Origin of This Text
　　This text has evolved from mathematics courses in the Master of Science in Computational Finance (MSCF) program at Carnegie Mellon University. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives precise statements of results, plausibility arguments, and even some proofs, but more importantly, intuitive explanations developed and refined through classroom experience with this material are provided. Exercises conclude every chapter. Some of these extend the theory and others are drawn from practical problems in quantitative finance. .
　　The first three chapters of Volume I have been used in a half-semester course in the MSCF program. The full Volume I has been used in a fullsemester course in the Carnegie Mellon Bachelor's program in Computational Finance. Volume II was developed to support three half-semester courses in the MSCF program.
　　Dedication
　　Since its inception in 1994, the Carnegie Mellon Master's program in Computational Finance has graduated hundreds of students. These people, who have come from a 9ariety of educational and professional backgrounds, have been a joy to teach. They have been eager to learn, asking questions that stimulated thinking, working hard to understand the material both theoretically and practically, and often requesting the inclusion of additional topics. Many came from the finance industry, and were gracious in sharing their knowledge in ways that enhanced the classroom experience for all.
　　This text and my own store of knowledge have benefited greatly from interactions with the MSCF students, and I continue to learn from the MSCF alumni. I take this opportunity to express gratitude to these students and former students by dedicating this work to them. ..
　　Acknowledgments
　　Conversations with several people, including my colleagues David Heath and Dmitry Kramkov, have influenced this text. Lukasz Kruk read much of the manuscript and provided numerous comments and corrections. Other students and faculty have pointed out errors in and suggested improvements of earlier drafts of this work. Some of these are Jonathan Anderson, Nathaniel Carter, Bogdan Doytchinov, David German, Steven Gillispie, Karel Janecek, Sean Jones, Anatoli Karolik, David' Korpi, Andrzej Krause, Rael Limbitco, Petr Luksan, Sergey Myagchilov, Nicki Rasmussen, Isaac Sonin, Massimo Tassan-Solet, David Whitaker and Uwe Wystup. In some cases, users of these earlier drafts have suggested exercises or examples, ,and their contributions are acknowledged at appropriate points in the text. To all those who aided in the development of this text, I am most grateful.
　　During the creation of this text, the author was partially supported by the National Science Foundation under grants DMS-9802464, DMS-0103814, and DMS-0139911. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation. ...
　　Pittsburgh, Pennsylvania, USA Steven E. Shreve
　　April 2004