Pricing Problem and Existance/Uniqueness of Backward Stochastic Differential Equations

In this paper, the option pricing problem in a complete financial market containing a bond and a finite number of stocks whose prices are driven by a multidimensional Brownian motion process, a multidimensional Poisson point process and a multidimensional Step point process is set. Under the frame of this market, we reduce the pricing problem to solution problem of a backward stochastic differential equation（BSDE）. Moreover, the existence and uniqueness of the solution of this BSDE are proven.