金融分析=Stochastic Calculus for Finance.第2卷 英文施瑞伍科技图书出版中心9787506272889蔚蓝书店 snb txt 网盘 pdf kindle 2025 lit 下载

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1 General Probability Theory

1.1 Infinite Probability Spacer/>

1.2 Random Variables and Distributionr/>

1.3 Expectationr/>

1.4 Convergence of Integralr/>

1.5 Computation of Expectationr/>

1.6 Change of Measure

1.7 Summary

1.8 Noter/>

1.9 Exerciser/>

2 Information and Conditioning

2.1 Information and or-algebrar/>

2.2 Independence

2.3 General Conditional Expectationr/>

2.4 Summary

2.5 Noter/>

2.6 Exerciser/>

3 Brownian Motion

3.1 Introduction

3.2 Scaled Random Walkr/>

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 Noter/>

3.10 Exerciser/>

4 Stochastic Calculur/>

4.1 Introduction

4.2 Itos Integral for Simple Integrandr/>

4.2.1 Construction of the Integral

4.2.2 Properties of the Integral

4.3 Itos Integral for General Integ-randr/>

4.4 Ito-Doeblin Formula

4.4.1 Formula for Brownian Motion

4.4.2 Formula for It6 Processer/>

4.4.3 Exampler/>

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 Evolutionr/>

4.5.4 Solution to the Black-Seholes-Merton Equation

4.5.5 The Greekr/>

4.5.6 Put-Call Parity

4.6 Multivariable Stochastic Calculur/>

4.6.1 Multiple Brownian Motionr/>

4.6.2 Ito-Doeblin Formula for Multiple Processer/>

4.6.3 Recognizing a Brownian Motion

4.7 Brownian Bridge

4.7.1 Gaussian Processer/>

4.7.2 Brownian Bridge as a Gaussian Procer/>

……

5 Risk-Neutral Pricing

6 Connections with Partial Differential Equationr/>

7 Exotic Optionr/>

8 American Derivative Securitier/>

9 Change of Numeraire

10 Term-Structure Modelr/>

11 Introduction to Jump Processer/>

A Advanced Topics in Probability Theory

B Existence of Conditional Expectationr/>

C Completion of the Proof of the Second Fundamental Theorem of Asset Pricing

Referencer/>

Index

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