Some Problems Of Backward Stochastic Differential Equations Driven By Continuous Martingales

Since E.Pardoux and S.Peng proposed the form of the Backward Stochastic Differential Equation ,the theory of the BSDEs obtained rapid development,and had the very good application in many domains like finance theory, recursion effectiveness, differential effectiveness,option pricing and so on in the economic theory .The classical Backward Stochastic Differential Equation theory is take the Brown motion as the noise source, but the Brown motion is one kind of extreme idealized model, causes the classical Backward Stochastic Differential Equation theory to receive certain limit in the application. In this paper ,its noise source by the Brown motion promotion for continuous martingale, discussed some issues of Backward Stochastic Differential Equation with continuous martingale.Since Skorohod,Stroock and VaradhanKrylov and so on proposed the weak solution concept for Stochastic Differential Equation, many scholars have made the unremitting effort in this aspect. Huang and Lin proposed the weak solution concept for Backward Stochastic Differential Equation This paper based on the predecessor's work , gives the weak solution concept for Backward Stochastic Differential Equation with continuous martingale,uses the Girsanov transformation, obtains its weak solution of the existence of a necessary and sufficient conditions, and on this basis obtains its weak solution of the existence of sufficient conditions,these sufficient conditions weakened the drifting coefficient which requested in the existence uniqueness of strong solution to satisfy the Lipschitz condition the request.The Option Pricing question is one of the core questions in the financial mathematics.In general,the thetraditional Option Pricing theory is Girsanov theorem and Martingale performance theorem of the stochastic analysis as a research tool. In the recent years, with the Backward Stochastic Differential Equation theory rapid development, Peng Shige has obtained the non-linear Feynman-Kac formula through the Backward Stochastic Differential Equation, and provided one new method for the Option Pricing. This paper works on the foundation of the predecessor,using the special nature of Ocone martingale and the conclusion which was obtained in the paper of Backward Stochastic Differential Equation with general martingale ,discussed the application of Backward Stochastic Differential Equation with ocone martingale to European option. Gave the determination price probability expression of the European option.