Some Studies On The Partial Differential Equation Theory And Numerical Solution In The Nonlinear Option Pricing Model

At present,the financial sector has become an important impetus to the development of domestic economy.The academic circles have made extensive research on the theory of financial field and made important contributions to the development and perfection of financial theory.At present,there are the agent theory,investment theory,option theory and the theory of market efficiency as the representatives for the financial theory.Among them,the option theory is one of the most widely used core knowledge systems in the field of financial capital transactions,which attracts extensive attention from researchers and the industry.With the development of market economy,option pricing becomes more and more complicated.How to enhance the reasonable pricing of options is an important issue in the field of option market research,and it is also the basis to maintain the stability of option market.Black-Scholes option pricing is the most widely used theory in option research.Since the advent of the theory,due to the greater optimization of the application value by the researchers attention.Black-Scholes option pricing plays an important role in today's financial market trade research.With the development of financial market,the process of option trading is more complicated,and the influence factors of option pricing are more diversified.If the traditional Black-Scholes option pricing method is still used,it is difficult to obtain high accuracy.There is a more serious bias,to investors prejudgment of the market adversely affected.Black-Scholes option pricing has become a core research topic in academia.In this paper,the Black-Scholes option pricing theory is deeply studied,and a variety of strategies including genetic algorithm,neural network algorithm and particle swarm optimization algorithm are used to modify Black-Scholes option pricing model,so that the model can apply to the actual marketing environment.