Backward Stochastic Differential Equations In Finance And Behavioral Finance

With the continuous development of financial market, discuss the theory of financial knowledge is becoming more and more thoroughly. In this paper, we mainly discuss the relevant and important theory of backward stochastic differential equation(BSDE) and its application in finance and behavioral finance.Backward stochastic differential equation is precisely embarks from the results of a process compared to traditional finance predict the trend of fure through the past experience, this kind of train of thought is more in line with the financial realities of rules. So this paper from the backward stochastic differential equations to review the professor Shige Peng,the French mathematician Pardoux and M. C. Quenez backward stochastic differential equation of the basic theorem briefly, important properties and backward stochastic differential equation in financial applications related discussion, through a combination of theoretical knowledge and practical examples draw a simple conclusion.On this basis, this paper also added to the related factors of behavior finance. The financial market in China is still in the initial development stage, compared with developed financial markets, with retail investors accounted for is relatively high, the institutional investors less, nonrational factors such as more features, thus the introduction of behavioral psychology, namely the psychology and finance were comprehensive research analysis, study on investor psychology factors, find the trend of investors behavior is appropriate, but also more in line with Chinese national conditions.This paper discussed the following three parts. The first part introduce the preliminary knowledge and basic theorem of stochastic differential equations and backward stochastic differential equations, and introduce some important results, such as the existence and uniqueness of the solution of backward stochastic differential equations, comparison theorem and so on. The second part introduced the european option pricing formula and the Black-Scholes formula firstly, and then, give some examples of backward stochastic differential equations in the pricing problem of the equation is linear and the portfolio with constraint conditions is nonlinear in the classical case. The third part introduces the basic viewpoint of behavioral finance and some financial models. What is more, makes some changes to the existing equations, and draws a conclusion. Specific, in the discrete case, mental function is brought into the binary tree, Use the application method for traditional binary tree to discuss with the psychological function of option pricing through the description of the traditional option pricing. Adding new psychological function in the backward stochastic differential equation to consider the price under the psychology of investors in the equation, and then analyze the new equations and draw new conclusions.