Backward Stochastic Differential Equations With Local Martingale

Backward and forward-backward stochastic differential equations with local martingale are presented in this paper. In chapter 2, existence and uniqueness results of the solutions of backward stochastic differential equations with local martingale under non-Lipschitz condition and local Lipschitz condition are first obtained, and some properties of backward stochastic differential equations with local martingale are further discussed. Finally, an example is given. In chapter 3, we first consider the existence and uniqueness results of the solutions of forward-backward stochastic differential equations with local martingale under Lipschitz condition, then get the comparison of FBSDE. The chapter 4 discussed the application of forward-backward stochastic differential equation with Ocone martingale to European option, and gave the determination price probability expression of the European option. In chapter 5, main contents of the paper are summarized.