金融衍生证券定价的随机分析基础

随机分析构成了金融衍生证券定价研究的重要理论基础与分析手段。尤其是几何布朗运动、算术布朗运动、均值恢复过程和Poisson跳跃过程等四类基本的随机过程和ITO随机微分定理得到了极其广泛的应用，可用以分析与解决几乎所有的金融衍生证券的定价问题。文章主要对这些基本的随机过程与随机分析方法及其在一般性Black-Scholes扩展定价模型推导中的应用进行分析与讨论，为解决更为复杂的金融衍生证券定价问题提供一个良好的理论研究框架。

Stochastic Analysis Foundation for Pricing Financial Derivative Securities

Stochastic analysis methods are an important theoretical foundation and analysis instrument for research on pricing financial derivative securities.Particularly, the four basic Stochastic process such as Geometric Brownian Motion,Arithmetric Brownian Motion,Mean Reverting Process and ITO theorem can get a more wide application.They could be used to analyze and solve almost all problems on pricing financial derivative securities.This paper mainly analyzes and discusses these basic stochastic process,stochastic methods,and their application in generally expanding Black scholes models,and gives a good theoretical research framework for the valuation of more complex financial derivative securities.