Stock Pricing Model Based On Stochastic System Theory

Financial market is a complex and ever-changing market.The price of financial assets is one of the most important factors in financial markets and naturally attracts great attention from investors.In recent years,there have been many methods for studying the price of securities.Financial mathematics has been favored by the academic community as a strong logical interdisciplinary subject.This article aims to build a stock price model through financial mathematics related theory and use this model for predictive analysis.This model is based on geometric Brownian motion,and innovatively adds Poisson jump parameter to the geometrical Brownian motion model to construct a dynamic model of stock price.Computer programming is used to implement the simulation process and make short-term predictions.Analyzes the similarity of statistical data between real data and forecast data,and verifies the rationality and effectiveness of the model.As one of the most important methods of stochastic process theory,the Brown Movement has a wide range of applications in predicting the price of financial assets.The 1997 B-S option pricing model that won the Nobel Prize in economics was based on the geometric Brownian movement.However,because of the continuity of geometric Brown orbits,there is no upward or downward discrete jump in the constructed price,which is different from the actual problem.In practical problems,due to various factors in the financial market,the price of securities will jump at a certain moment,and the Poisson process will naturally be applied to this problem as a process with a jump.Based on the characteristics of China's A-share market,this article has established a set of stock data sets including the Shanghai Composite Index,the Shanghai and Shenzhen 300 and China Ping An,etc.to verify the model.This paper uses the maximum likelihood estimation method to calculate the parameters ? and? in the model.By defining different Poisson jump heights to calculate the value of?,a different prediction result is obtained.