金融随机分析(第2卷)(英文版)
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作者(美)施瑞伍|责编:刘慧//高蓉
出版社世界图书出版公司
ISBN9787506272889
出版时间2007-04
装帧其他
开本其他
定价129元
货号30940128
上书时间2024-07-03
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目录
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 o-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 Integrands
4.4 Ito-Doeblin Formula
4.4.1 Formula for Brownian Motion
4.4.2 Formula for Ito 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-Scholes-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
4.7.3 Brownian Bridge as a Scaled Stochastic Integral
4.7.4 Multidimensional Distribution of the Brownian Bridge
4.7.5 Brownian Bridge as a Conditioned Brownian Motion
4.8 Summary
4.9 Notes
4.10 Exercises
5 Risk-Neutral Pricing
5.1 Introduction
5.2 Risk-Neutral Measure
5.2.1 Girsanov's Theorem for a Single Brownian Motion
5.2.2 Stock Under the Risk-Neutral Measure
5.2.3 Value of Portfolio Process Under the Risk-Neutral Measure
5.2.4 Pricing Under the Risk-Neutral Measure
5.2.5 Deriving the Black-Scholes-Merton Formula
5.3 Martingale Representation Theorem
5.3.1 Martingale Representation with One Brownian Motion
5.3.2 Hedging with One Stock
5.4 Fundamental Theorems of Asset Pricing
5.4.1 Girsanov and Martingale Representation Theorems
5.4.2 Multidimensional Market Model
5.4.3 Existence of the Risk-Neutral Measure
5.4.4 Uniqueness of the Risk-Neutral Measure
5.5 Dividend-Paying Stocks
5.5.1 Continuously Paying Dividend
5.5.2 Continuously Paying Dividend with Constant Coefficients
5.5.3 Lump Payments of Dividends
5.5.4 Lump Payments of Dividends with Constant Coefficients
5.6 Forwards and Futures
5.6.1 Forward Contracts
5.6.2 Futures Contracts
5.6.3 Forward-Futures Spread
5.7 Summary
5.8 Notes
5.9 Exercises
6 Connections with Partial Differential Equations
6.1 Introduction
6.2 Stochastic Differential Equations
6.3 The Markov Property
6.4 Partial Differential Equations
内容摘要
本书为《金融随机分析》的第2卷，主要包括：连续时间模型和该模型经济学中的应用。
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