金融随机分析（第2卷）
2007-4
北京世图
施瑞伍
550
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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 Exercises2 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 Exercises3 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 Exercises4 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 Pricing6 Connections with Partial Differential Equations7 Exotic Options8 American Derivative Securities 9 Change of Numeraire10 Term-Structure Models11 Introduction to Jump ProcessesA Advanced Topics in Probability TheoryB Existence of Conditional ExpectationsC Completion of the Proof of the Second Fundamental Theorem of Asset PricingReferences Index
《金融随机分析(第2卷)》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。
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