The Research And Application Of Solution Of Two Types Of Backward Stochastic Differential Equation

In 1973, the French mathematician Bismut introduced a linear backward stochastic differential equations into the study of optimal control, and made a systematic study. In the early 1990 s, Chinese mathematician Peng Shige and French mathematician Pardoux published an article named "backward stochastic differential equations to the solution", witch introduced the theory of nonlinear backward stochastic differential equations at first time. After that, BSDE has gradually been a very active field, which have attracted more scholars for further research. Excepting itself theory of the BSDEs, its important application background also have become the study field for lots of scholars.With the reference in the literature, in the present study, the related properties of the solution of backward stochastic differential equation and its application were studied.In the first chapter,this paper mainly introduces the background of the topic and related marks.In the second chapter, the article mainly discussed the existence and uniqueness,stability, comparison theorem of BSDE’s solution under non Lipschitz condition.In chapter three, this paper mainly discusses the properties of a new type of backward doubly stochastic differential equation, and obtained the existence and uniqueness of the solution, comparison theorem under non Lipschitz condition.In chapter four, the article mainly researched the backward stochastic differential equation in the insurance pricing application. In this paper, the related theory of insurance are introduced, and then summarized the insurance pricing theory of backward stochastic differential equations, in order to establish the mathematical model of the original insurance and reinsurance. At last, we deduced the pricing formula.