声明
摘要
Abstract
Contents
Chapter 1 Introduction
1．1 Overview
1．2 Background of the Mathematical Modeling of Risky Asset Prices
1．3 Why Fractional Brownian Motion is used in this thesis?
1．4 A Brief Introduction of Baidu and Tencent Companies
Chapter 2 Stochastic Calculus
2．1 Introduction
2．2 Preliminaries and Definitions
2．3 Brownian Motion
2．4 Ito Processes and Ito Formula
2．5 Stochastic Differential Equations
Chapter 3 Fractional Stochastic
3．1 Introduction
3．2 Long Memory and Short Memory
3．3 Fractional Brownian Motion
3．3．1 Basic Definitions
3．3．2 A Fractional Brownian Motion Is Not A Semimartingale
3．3．3 A Fractional Brownian Motion Is Not A Markov Process
3．4 Fractional Black-Scholes Model
Chapter 4 Mathematical Modeling
4．1 Introduction
4．2 Estimation of Return and volatility
4．3 Mathematical Modeling of Stock Prices
4．4 Conclusion
Appendix
Resources
Acknowledgments
