《金融隨機分析》這是一套隨機分析在定量經(jīng)濟學領域中應用方面的著名教材，作者在該領域享有盛譽，全書共分2卷。第1卷主要包括隨機分析的基礎性知識和離散時間模型；第2卷主要包括連續(xù)時間模型和該模型經(jīng)濟學中的應用。就其內容而言，第2卷有較為實際的可操作性的定量經(jīng)濟學內容，同時也包含了較為完整的隨機微分方程理論。
《金融隨機分析(第2卷)》各章有習題，適用于掌握微積積分基礎知識的大學高年級本科生和碩士研究生。
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
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 Itos Integral for Simple Integrands
4.2.1 Construction of the Integral
4.2.2 Properties of the Integral
4.3 Itos 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
Index
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