Stochastic Differential Equations And Its Application

For this kind of backward stochastic differential equation as followsY_t =ξ∫_t~T+ g(s,Y_s,Z_s)ds-∫_t~T Z_sdW_sWhere ξis the terminal condition, a pair of process (Y,Z)is the solution satisfying this equation. These equations were first introduced by Bismut(1973) inthe linear case and by Parodoux and Peng(1989) . In this article, we discuss the solution ofbackward stochastic differential equation and the generalizes comparison theorem and concernedthe relation between g-Expection and the minimum expection. At last we give the application ofBSDE in finance.