金融工程圣经：Stochastic calculus for finance II - Continuous - time models

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<br/> 内容简介 <p>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。<br/>  本书各章有习题，适用于掌握微积分基础知识的大学高年级本科生和硕士研究生。</p>作者简介 <p>Steven E. Shreve is Co-Founder of the Carnegie Mellon MS Program in Computational Finance and winner of the Carnegie Mellon Doherty Prize for sustained contributions to education. </p>在Amazon.com上面的书评： <p>"Steven Shreve’s comprehensive two-volume Stochastic Calculus for Finance may well be the last word, at least for a while, in the flood of Master’s level books.... a detailed and authoritative reference for "quants” (formerly known as "rocket scientists”). The books are derived from lecture notes that have been available on the Web for years and that have developed a huge cult following among students, instructors, and practitioners. The key ideas presented in these works involve the mathematical theory of securities pricing based upon the ideas of classical finance.<br/>...the beauty of mathematics is partly in the fact that it is self-contained and allows us to explore the logical implications of our hypotheses. The material of this volume of Shreve’s text is a wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions.<br/>In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach. It is accessible to a broad audience and has been developed after years of teaching the subject. It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." (SIAM, 2005)</p><p>"The contents of the book have been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise Statements of results, plausibility arguments, and even some proofs. But more importantly, intuitive explanations, developed and refine through classroom experience with this material are provided throughout the book." (Finanz Betrieb, 7:5, 2005)</p><p>"The origin of this two volume textbook are the well-known lecture notes on Stochastic Calculus … . The first volume contains the binomial asset pricing model. … The second volume covers continuous-time models … . This book continues the series of publications by Steven Shreve of highest quality on the one hand and accessibility on the other end. It is a must for anybody who wants to get into mathematical finance and a pleasure for experts … ." (www.mathfinance.de, 2004)</p><p>"This is the latter of the two-volume series evolving from the author’s mathematics courses in M.Sc. Computational Finance program at Carnegie Mellon University (USA). The content of this book is organized such as to give the reader precise statements of results, plausibility arguments, mathematical proofs and, more importantly, the intuitive explanations of the financial and economic phenomena. Each chapter concludes with summary of the discussed matter, bibliographic notes, and a set of really useful exercises." (Neculai Curteanu, Zentralblatt MATH, Vol. 1068, 2005)</p><p></p><br/>

[此贴子已经被作者于2008-5-29 17:06:52编辑过]

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关键词：Stochastic Continuous Calculus Stochast Finance Finance 圣经 Calculus Stochastic Continuous

目录信息

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
3.2.1 Symmetric Random "Walk
3.2.2 Increments of the Symmetric Random Walk
3.2.3 Martingale Property for the Symmetric Random Walk
3.2.4 Quadratic Variation of the Symmetric Random Walk
3.2.5 Scaled Symmetric Random Walk
3.2.6 Limiting Distribution of the Scaled Random Walk
3.2.7 Log-Normal Distribution as the Limit of the Binomial Model
　3.3 Brownian Motion
3.3.1 Definition of Brownian Motion
3.3.2 Distribution of Brownian Motion
3.3.3 Filtration for Brownian Motion
3.3.4 Martingale Property for Brownian Motion
　3.4 Quadratic Variation
3.4.1 First-Order Variation
3.4.2 Quadratic Variation
3.4.3 Volatility of Geometric Brownian Motion
　3.5　Markov Property
　3.6 First Passage Time Distribution
　3.7 Reflection Principle
3.7.1 Reflection Equality
3.7.2 First Passage Time Distribution
3.7.3 Distribution of Brownian Motion and Its Maximum
　3.8 Summary
　3.9 Notes
　3.10 Exercises
4 Stochastic Calculus
　4.1 Introduction
　4.2 Ito's Integral for Simple Integrands
4.2.1 Construction of the Integral
4.2.2 Properties of the Integral
　4.3 Ito's Integral for General Integ-rands
　4.4 Ito-Doeblin Formula
4.4.1 Formula for Brownian Motion
4.4.2 Formula for It6 Processes
4.4.3 Examples
　4.5 Black-Scholes-Merton Equation
4.5.1 Evolution of Portfolio Value
4.5.2 Evolution of Option Value
4.5.3 Equating the Evolutions
4.5.4 Solution to the Black-Seholes-Merton Equation
4.5.5 The Greeks
4.5.6 Put-Call Parity
　4.6 Multivariable Stochastic Calculus
4.6.1 Multiple Brownian Motions
4.6.2 Ito-Doeblin Formula for Multiple Processes
4.6.3 Recognizing a Brownian Motion
　4.7 Brownian Bridge
4.7.1 Gaussian Processes
4.7.2 Brownian Bridge as a Gaussian Process
……
5 Risk-Neutral Pricing
6 Connections with Partial Differential Equations
7 Exotic Options
8 American Derivative Securities
9 Change of Numeraire
10 Term-Structure Models
11 Introduction to Jump Processes
A Advanced Topics in Probability Theory
B Existence of Conditional Expectations
C Completion of the Proof of the Second Fundamental Theorem of Asset Pricing
References

谢谢楼主,请问有没有这本书的   SOLUTION MANUAL,如果有的话请上传,可以的话请发到我的邮箱alexshen2@gmail.com.谢谢