中文摘要：

本文把证券市场中的投资者分为Ⅰ型和Ⅱ型两类.建立起Ⅰ类投资价格过程模型并简要论述了其收敛性,对连续渗流模型进行了介绍,运用连续渗流理论建立起Ⅱ类投资价格过程模型并研究了该价格模型波动的统计特性,揭示了价格过程的特征函数收敛于Black-Scholes模型相应的特征函数,最后,文章讨论了该价格模型下欧式未定权益的定价和套期保值问题。

英文摘要：

This paper considers two types of investors in a stock market--group I and group II. It constructs the type I stock price process model and discusses its convergence briefly. The paper gives a simple intro- duction for continuum percolation theory. It constructs the type II stock price process model by continuum percolation methods and investigates the statistical properties of the fluctuations of this model. It shows that the characteristic function of this stock price process converges to the corresponding characteristic function of the Black-Scholes model. Finally, the paper discusses the valuation and hedging of European contingent claims.