Stock Prices Fluctuations and Analytical Valuation of Contingent Claims by Stochastic Interacting Systems

In this paper, applying the theory of stochastic processes and interacting particle systems, including stopping time theory and the stochastic voter model, we model a financial price model that contains two types of investors, and we use this financial model to describe the behavior and fluctuations of a stock price process in a stock market. In the financial model, besides the professional investors, we also consider the general investors or nonprofessional investors, where the stopping time and the voter model are applied to model and study the statistical properties of investment of the nonprofessional investors. Further, we discuss the valuation and hedging of European contingent claims for this price process model.